DEVELOPMENT OF RAPID ASSESSMENT TOOLS 
FOR GROUNDWATER VULNERABILITY MAPPING 
USING INTEGRATED GEOSCIENTIFIC DATASETS 
AND ARTIFICIAL INTELLIGENCE ALGORITHMS: 
CASE STUDY FROM WITBANK AND ERMELO 
COALFIELDS, SOUTH AFRICA 
 
 
Emmanuel Sakala 
 
 
Submitted in fulfilment of the requirements for the degree 
 
Philosophiae Doctor 
 
in the 
Faculty of Natural and Agricultural Sciences 
(Institute for Groundwater Studies) 
at the 
University of the Free State 
 
 
Supervisor: Dr Francois Fourie 
 
 
2017 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Our intelligence is what makes us human, and artificial intelligence is an 
extension of that quality. 
 
YANN LECUN 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 DECLARATION 
I, Emmanuel SAKALA, hereby declare that the thesis hereby submitted by me to the Institute for 
Groundwater Studies in the Faculty of Natural and Agricultural Sciences at the University of the Free 
State, in fulfilment of the degree of Doctor Philosophiae, is my own independent work. It has not 
previously been submitted by me to any other institution of higher education. In addition, I declare 
that all sources cited have been acknowledged by means of a list of references. 
I furthermore cede copyright of the thesis and its contents in favour of the University of the Free State 
and the Council for Geoscience. 
 
 
 
Emmanuel SAKALA 
18 April 2018 
  
 
 
 
ACKNOWLEDGEMENTS 
First, I want to thank Almighty God for having given me strength through this period. 
A special thank you to my supervisor Dr Francois Fourie for assistance, guidance and patience during 
this research period. Your inputs through advice, data analysis and eventually right through the final 
write up of the dissertation are highly appreciated. 
Another special thank you goes to Dr Modreck Gomo for help with the geochemical and 
hydrogeological interpretation of the data. 
The thesis emanated from the Mine Water Management Project, funded under the Medium Term 
Expenditure Framework by the Department of Mineral Resources (DMR) of South Africa. I wish to 
extend a sincere thank you to the DMR and the Council for Geoscience for allowing me to do the 
research that I am positive will have a valuable impact on the entire nation. Thank you to Dr Henk 
Coetzee, the project manager of the Mine Water Management project for allowing me to be part of 
the project team. 
Editorial assistance by Dr Vunganai Midzi, Ms Zahn Nel, Dr Godfrey Madzivire and Mr Emmanuel 
Chirenje is greatly appreciated. 
My gratitude for help with Python programming goes to Mr Patrick Cole and the Stock Overflow 
online community. 
I would like to thank my family for your support during many late nights and when I was away from 
home on field trips during the course of the research. Thank you also to my friends for your support 
and encouragement. 
My sincere thanks goes to the Council for Geoscience geophysics and remote sensing team for 
invaluable assistance with fieldwork and to the laboratory unit for making their facilities available. 
Finally, I would like to extend my sincerest gratitude to everyone with whom I did not mention by 
name but who contributed to the fulfilment of this dissertation. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
To my beloved wife Joyce and my son Tinashe 
 
 
 
 
 
 
TABLE OF CONTENTS 
 
List of Acronyms ............................................................................................................................................................. i 
Measurement Units ....................................................................................................................................................... iv 
Outcomes of the Research .............................................................................................................................................. v 
CHAPTER 1 : INTRODUCTION .................................................................................................... 1 
1.1 Background ....................................................................................................................................................... 1 
1.2 Aims and Objectives ......................................................................................................................................... 4 
1.3 Outline of Research Methodology .................................................................................................................... 5 
1.4 Limitations of the Research ............................................................................................................................... 6 
1.5 Structure of the Thesis....................................................................................................................................... 7 
CHAPTER 2 : GROUNDWATER VULNERABILITY ASSESSMENT METHODS ............... 9 
2.1 Introduction ....................................................................................................................................................... 9 
2.2 General Concept of Groundwater Vulnerability ............................................................................................... 9 
2.2.1 Laws of Groundwater Vulnerability ................................................................................................................ 10 
2.3 Review of Groundwater Vulnerability Assessment Approaches .................................................................... 11 
2.3.1 Overlay and Index Approach ........................................................................................................................... 11 
2.3.1.1 DRASTIC ............................................................................................................................................................ 11 
2.3.1.2 GOD .................................................................................................................................................................... 14 
2.3.1.3 SINTACS ............................................................................................................................................................ 15 
2.3.1.4 AVI ...................................................................................................................................................................... 16 
2.3.2 Process-Based Simulation Modelling .............................................................................................................. 17 
2.3.3 Statistical Approaches...................................................................................................................................... 18 
2.4 Acid Mine Drainage Formation Processes ...................................................................................................... 18 
2.5 Shortcomings of Groundwater Vulnerability Assessment Methods ............................................................... 20 
2.6 Overview of Artificial Intelligence Systems ................................................................................................... 21 
2.7 Applications of Artificial Intelligence in Groundwater Vulnerability Assessments ....................................... 23 
2.8 Globally Accepted Regional Assessment Approaches .................................................................................... 25 
2.8.1 Mineral Systems Approach .............................................................................................................................. 26 
2.8.2 Petroleum Systems ........................................................................................................................................... 27 
2.8.3 Source-Transport-Attenuation Approach ......................................................................................................... 28 
2.9 Summary ......................................................................................................................................................... 28 
CHAPTER 3 : DEVELOPMENT OF GIS-BASED GROUNDWATER VULNERABILITY 
ASSESSMENT FOR ACID MINE DRAINAGE .......................................................................... 30 
3.1 Introduction ..................................................................................................................................................... 30 
3.2 Overview of the SPT Approach ...................................................................................................................... 30 
3.3 The SPT Input Map Layers ............................................................................................................................. 32 
3.3.1 Sources ............................................................................................................................................................. 32 
3.3.1.1 Sources of energy ................................................................................................................................................ 33 
3.3.1.2 Sources of ligands (water) ................................................................................................................................... 35 
3.3.1.3 Mappable sources of AMD pollution ................................................................................................................... 36 
3.3.1.4 Subsurface sources of pollution ........................................................................................................................... 36 
3.3.2 Transportation Pathway ................................................................................................................................... 36 
3.3.2.1 Transportation pathway in soils ........................................................................................................................... 36 
3.3.2.2 Transport in the vadose zone ............................................................................................................................... 37 
3.3.2.2.1 Preferential pathways ................................................................................................................... 37 
3.3.2.2.2 Rock permeability ......................................................................................................................... 37 
3.3.2.3 Transport in the aquifer system ............................................................................................................................ 37 
3.3.3 AMD Pollution Traps ...................................................................................................................................... 38 
3.3.3.1 Chemical traps of acid mine drainage in soils ...................................................................................................... 38 
3.3.3.2 Pollution traps in the vadose zone and aquifer media .......................................................................................... 39 
 
 
 
3.3.3.2.1 Depth to water table ...................................................................................................................... 39 
3.3.3.2.2 Rock-AMD reactivity..................................................................................................................... 39 
3.3.4 SPT Groundwater Vulnerability Modelling ..................................................................................................... 39 
3.4 Generation of SPT Input Map Layers for the Witbank, Ermelo and Highveld Coalfields .............................. 40 
3.4.1 Location of the Witbank, Ermelo and Highveld Coalfields ............................................................................. 40 
3.4.1.1 Location of the Witbank coalfield ....................................................................................................................... 40 
3.4.1.2 Location of the Highveld coalfield ...................................................................................................................... 41 
3.4.1.3 Location of the Ermelo coalfield ......................................................................................................................... 41 
3.4.2 Physiography ................................................................................................................................................... 42 
3.4.3 Geological and Hydrogeological Setting ......................................................................................................... 43 
3.4.3.1 Regional geology ................................................................................................................................................. 43 
3.4.3.2 Local geological setting ....................................................................................................................................... 45 
3.4.3.2.1 The Basement Complex ................................................................................................................. 46 
3.4.3.2.2 The Witwatersrand Supergroup .................................................................................................... 47 
3.4.3.2.3 The Transvaal Supergroup ............................................................................................................ 47 
3.4.3.2.4 Bushveld Igneous Complex ........................................................................................................... 48 
3.4.3.2.5 Waterberg Group .......................................................................................................................... 49 
3.4.3.2.6 Karoo Supergroup ........................................................................................................................ 49 
3.4.3.2.7 Quaternary deposits ...................................................................................................................... 50 
3.4.3.3 Hydrogeological setting ....................................................................................................................................... 51 
3.4.3.3.1 Aquifer types ................................................................................................................................. 51 
3.4.3.3.2 Hydrochemistry ............................................................................................................................. 55 
3.4.4 Mining Activities and their Contribution to AMD Pollution ........................................................................... 58 
3.4.4.1 Coal mining history of the Witbank, Ermelo and Highveld coalfields ................................................................ 58 
3.4.4.2 Coal geology ........................................................................................................................................................ 59 
3.4.4.2.1 Witbank coalfield .......................................................................................................................... 59 
3.4.4.2.2 Highveld coalfield ......................................................................................................................... 59 
3.4.4.2.3 Ermelo coalfield ............................................................................................................................ 59 
3.4.4.3 Coal mining activities and their impacts to the environment ............................................................................... 60 
3.4.5 SPT Inputs for the Witbank, Ermelo and Highveld Coalfields ........................................................................ 61 
3.4.5.1 Sources of energy (topographic slope) ................................................................................................................. 61 
3.4.5.2 Sources of ligands (water) ................................................................................................................................... 62 
3.4.5.3 Surface sources of AMD pollution ...................................................................................................................... 65 
3.4.5.3.1 Methodology for identification of AMD surface sources .............................................................. 65 
3.4.5.3.2 Results and discussions ................................................................................................................. 71 
3.4.5.4 Subsurface sources............................................................................................................................................... 76 
3.4.5.5 Transport and attenuation in the soils .................................................................................................................. 76 
3.4.5.5.1 Materials and methods .................................................................................................................. 80 
3.4.5.5.2 Experimental results and discussion ............................................................................................. 83 
3.4.5.6 Preferential pathways ........................................................................................................................................... 88 
3.4.5.7 Rock permeability ................................................................................................................................................ 92 
3.4.5.8 Hydraulic conductivity ........................................................................................................................................ 93 
3.4.5.9 Depth to water table ............................................................................................................................................. 94 
3.4.5.10 Rock-AMD reactivity .......................................................................................................................................... 95 
3.4.5.10.1 Materials and methods ................................................................................................................ 96 
3.4.5.10.2 Sample mineralogy results and discussions ................................................................................ 98 
3.4.5.10.3 Experimental results and discussion ......................................................................................... 103 
3.4.5.10.4 Summary ................................................................................................................................... 113 
3.5 Summary ....................................................................................................................................................... 116 
CHAPTER 4 : KNOWLEDGE-DRIVEN FUZZY EXPERT SYSTEM .................................. 118 
4.1 Introduction ................................................................................................................................................... 118 
4.2 Knowledge-Driven Artificial Intelligence Systems ...................................................................................... 118 
4.3 Overview of Fuzzy Expert Systems .............................................................................................................. 118 
4.3.1 Fuzzification .................................................................................................................................................. 119 
4.3.2 Fuzzy Inference Engine ................................................................................................................................. 120 
4.3.2.1 Fuzzy (AND) operation ..................................................................................................................................... 120 
 
 
 
4.3.2.2 Fuzzy (OR) operation ........................................................................................................................................ 120 
4.3.2.3 Fuzzy (SUM) operator ....................................................................................................................................... 121 
4.3.2.4 Fuzzy (PRODUCT) operator ............................................................................................................................. 121 
4.3.2.5 Fuzzy (GAMMA) operator ................................................................................................................................ 122 
4.3.3 Defuzzification .............................................................................................................................................. 122 
4.4 Application of the Fuzzy Expert System to Groundwater Vulnerability Assessment ................................... 122 
4.4.1 Cognitive Reasoning ...................................................................................................................................... 123 
4.4.1.1 Sources factor .................................................................................................................................................... 123 
4.4.1.1.1 Energy sources ............................................................................................................................ 123 
4.4.1.1.2 Ligand (water) sources ............................................................................................................... 123 
4.4.1.1.3 Pollutant sources ........................................................................................................................ 123 
4.4.1.2 Transportation pathway factor ........................................................................................................................... 124 
4.4.1.3 Traps .................................................................................................................................................................. 124 
4.5 Fuzzy Expert System: Application to the Witbank, Ermelo and Highveld Coalfields .................................. 124 
4.5.1 Fuzzification .................................................................................................................................................. 124 
4.5.1.1 Assigning map weights, class weights and confidence factors for the sources factor ........................................ 126 
4.5.1.2 Assigning map weights, class weights and confidence factors for the transportation pathway factor ............... 127 
4.5.1.3 Assigning map weights, class weights and confidence factors for the traps factor ............................................ 128 
4.5.2 Fuzzy Inference Engine ................................................................................................................................. 128 
4.5.2.1 Sources factor input (S) ..................................................................................................................................... 129 
4.5.2.2 Transportation pathway factor input (P) ............................................................................................................ 134 
4.5.2.3 Traps factor input (T) ......................................................................................................................................... 139 
4.5.2.4 Resultant fuzzy output model ............................................................................................................................ 142 
4.5.3 Defuzzification .............................................................................................................................................. 143 
4.5.4 Model Validation of the Fuzzy Expert System .............................................................................................. 145 
4.5.4.1 Model validation using hydrochemistry data ..................................................................................................... 145 
4.5.4.1.1 Correlation coefficient approach ................................................................................................ 145 
4.5.4.1.2 Cross-section method of validation ............................................................................................. 146 
4.5.4.2 Validation using geophysical techniques ........................................................................................................... 148 
4.5.4.2.1 Materials and methods ................................................................................................................ 148 
4.5.4.2.2 Results and discussion ................................................................................................................ 151 
4.5.4.2.3 Summary ..................................................................................................................................... 157 
4.6 Discussion ..................................................................................................................................................... 158 
4.7 Summary ....................................................................................................................................................... 159 
CHAPTER 5 : DATA PREPARATION AND AUTOMATION FOR DATA-DRIVEN 
ARTIFICIAL INTELLIGENCE MODELLING ....................................................................... 160 
5.1 Introduction ................................................................................................................................................... 160 
5.2 Selection of Training Sites ............................................................................................................................ 160 
5.3 Model Selection ............................................................................................................................................ 160 
5.3.1 Spatial Association Testing of Input Map Layers .......................................................................................... 161 
5.3.1.1 Ligand water sources (rainfall) layer ................................................................................................................. 162 
5.3.1.2 Energy sources (slope) layer .............................................................................................................................. 164 
5.3.1.3 Surface sources of AMD layer ........................................................................................................................... 165 
5.3.1.4 Subsurface sources of AMD layer ..................................................................................................................... 166 
5.3.1.5 Soil clay content layer ....................................................................................................................................... 168 
5.3.1.6 Preferential pathway layer ................................................................................................................................. 169 
5.3.1.7 Aquifer hydraulic conductivity layer ................................................................................................................. 171 
5.3.1.8 Rock permeability layer ..................................................................................................................................... 172 
5.3.1.9 Rock-AMD reactivity layer ............................................................................................................................... 173 
5.3.1.10 Depth to water table layer .................................................................................................................................. 174 
5.3.2 Determination of Optimal Data-Driven Model Parameters ........................................................................... 177 
5.3.2.1 Epoch determination algorithm for data-driven approaches .............................................................................. 177 
5.3.2.2 Hidden layer neuron number determination algorithm for data-driven approaches ........................................... 177 
5.3.2.3 Data splitting algorithms .................................................................................................................................... 177 
5.4 Discussion ..................................................................................................................................................... 178 
5.5 Summary ....................................................................................................................................................... 179 
 
 
 
CHAPTER 6 : DATA-DRIVEN ARTIFICIAL NEURAL NETWORK SYSTEM ................. 180 
6.1 Introduction ................................................................................................................................................... 180 
6.2 Overview of Data-Driven Artificial Neural Network systems ...................................................................... 180 
6.2.1 Biological Neural Network Background........................................................................................................ 180 
6.2.2 Artificial Neural Network Background.......................................................................................................... 181 
6.2.3 History of ANNs ............................................................................................................................................ 184 
6.2.4 Architecture of ANNs .................................................................................................................................... 185 
6.2.5 Learning by ANNs ......................................................................................................................................... 187 
6.2.5.1 Supervised training ............................................................................................................................................ 187 
6.2.5.2 Unsupervised training ........................................................................................................................................ 187 
6.2.5.3 Hybrid training .................................................................................................................................................. 188 
6.2.6 Learning Algorithms – Backpropagation using a Sigmoid Activation Function ........................................... 188 
6.2.6.1 Feed-forward computation ................................................................................................................................. 188 
6.2.6.2 Back propagation to the output layer ................................................................................................................. 188 
6.2.6.3 Back propagation to the hidden layer ................................................................................................................ 190 
6.2.7 Types of Artificial Neural Networks ............................................................................................................. 190 
6.2.7.1 Feed-forward ANNs .......................................................................................................................................... 190 
6.2.7.2 Recurrent ANNs ................................................................................................................................................ 191 
6.3 Data-Driven Artificial Neural Network: Application to the Witbank, Ermelo and Highveld Coalfields ...... 191 
6.3.1 ANN Training ................................................................................................................................................ 192 
6.3.1.1 Selection of training sites ................................................................................................................................... 192 
6.3.1.2 Binary map creation ........................................................................................................................................... 192 
6.3.1.3 Establishing the optimum number of epochs and neurons in the hidden layer .................................................. 193 
6.3.1.4 Selection of cross-validation method ................................................................................................................. 194 
6.3.1.5 Artificial neural network modelling ................................................................................................................... 194 
6.3.2 Data-Driven ANN Model Results .................................................................................................................. 196 
6.3.3 Validation of the ANN Model ....................................................................................................................... 198 
6.3.3.1 Model validation using hydrochemistry data ..................................................................................................... 198 
6.3.3.1.1 Correlation coefficient approach ................................................................................................ 198 
6.3.3.1.2 Cross-section method of validation ............................................................................................. 199 
6.3.3.2 Validation using geophysical techniques ........................................................................................................... 200 
6.4 Discussion ..................................................................................................................................................... 201 
6.5 Summary ....................................................................................................................................................... 202 
CHAPTER 7 : HYBRID ARTIFICIAL INTELLIGENCE SYSTEM ..................................... 203 
7.1 Introduction ................................................................................................................................................... 203 
7.2 Overview of the Hybrid System .................................................................................................................... 203 
7.2.1 Types of Neuro-Fuzzy Systems ..................................................................................................................... 203 
7.2.1.1 Neural-fuzzy systems ......................................................................................................................................... 204 
7.2.1.2 Fuzzy-neural systems ......................................................................................................................................... 204 
7.2.1.3 Hybrid neuro-fuzzy systems .............................................................................................................................. 205 
7.2.1.3.1 ANFIS system operation.............................................................................................................. 206 
7.2.1.3.2 Learning algorithm of the ANFIS ............................................................................................... 208 
7.3 The ANFIS System for Groundwater Vulnerability Assessments: Application to the Witbank, Ermelo and 
Highveld Coalfields .......................................................................................................................................... 212 
7.3.1 Design Step of the ANFIS for Groundwater Vulnerability............................................................................ 212 
7.3.1.1 Selection of system inputs and outputs .............................................................................................................. 212 
7.3.1.2 ANFIS system training ...................................................................................................................................... 213 
7.3.2 Hybrid System Model Results ....................................................................................................................... 214 
7.3.3 Validation of the ANFIS Model .................................................................................................................... 216 
7.3.3.1 Model validation using hydrochemistry data ..................................................................................................... 216 
7.3.3.1.1 Correlation coefficient approach ................................................................................................ 216 
7.3.3.1.2 Validation using the cross-section method.................................................................................. 217 
7.3.3.2 Validation using geophysical techniques ........................................................................................................... 218 
7.4 Discussion ..................................................................................................................................................... 219 
7.5 Summary ....................................................................................................................................................... 220 
 
 
 
CHAPTER 8 : TOOLBOX FOR RAPID ASSESSMENT OF GROUNDWATER 
VULNERABILITY ........................................................................................................................ 221 
8.1 Introduction ................................................................................................................................................... 221 
8.2 Overview of the Toolbox .............................................................................................................................. 221 
8.2.1 Main Menu Module ....................................................................................................................................... 223 
8.2.2 Data Input Module ......................................................................................................................................... 223 
8.2.3 Fuzzy Expert System Module ........................................................................................................................ 224 
8.2.4 Data Pre-Processing Module for Data-Driven AI Systems ............................................................................ 226 
8.2.5 ANN Module ................................................................................................................................................. 227 
8.2.6 ANFIS Module .............................................................................................................................................. 229 
8.2.7 Model Validation Module .............................................................................................................................. 231 
8.3 Discussion and Summary .............................................................................................................................. 232 
CHAPTER 9 : CONCLUSIONS AND RECOMMENDATIONS ............................................. 234 
9.1 Concluding Remarks...................................................................................................................................... 234 
9.1.1 Development of AMD Specific Groundwater Vulnerability Approach ........................................................ 234 
9.1.2 Laboratory and Field Experiments for Groundwater Vulnerability Input Selection and Model Validation .. 235 
9.1.3 Application of AI to the Assessment of Groundwater Vulnerability Specific for Coalfields ........................ 235 
9.1.4 Groundwater Vulnerability Graphic User Interface Toolbox ........................................................................ 236 
9.2 Recommendations .......................................................................................................................................... 237 
9.2.1 General Recommendations ............................................................................................................................ 237 
9.2.2 Limitations of the Developed Data-Driven Approaches ................................................................................ 237 
9.2.3 Recommendations for Future Work ............................................................................................................... 238 
REFERENCES ............................................................................................................................... 240 
APPENDICES 
Appendix 1: Soil Batch Leach Experiment ................................................................................................................ 254 
Appendix 1.1 Results of leachate analysis after the soil batch leach with AMD ...................................................... 254 
Appendix 1.2 Results of leachate analysis after the soil batch leach with de-ionised water ..................................... 254 
Appendix 1.3 Results of major elements of soil samples analysed by XRF ............................................................. 254 
Appendix 2: Rock-AMD Column Leach Experiment ................................................................................................ 255 
Appendix 2.1 Results of chemical analysis of leachate under saturated conditions .................................................. 255 
Appendix 2.2 Results of chemical analysis of leachate under unsaturated conditions .............................................. 256 
Appendix 2.3 Results of the mineralogical analysis of rock samples by XRD ......................................................... 257 
Appendix 2.4 Results of the XRF analysis of the major elements of rock samples .................................................. 257 
Appendix 3: Determination of Optimal Data-Driven Model Parameters ................................................................... 258 
Appendix 3.1: Epoch determination algorithm for data-driven approaches .......................................................................... 258 
Appendix 3.2: Hidden layer neuron number determination algorithm for data-driven approaches ....................................... 259 
Appendix 3.3: Data splitting algorithms ............................................................................................................................... 260 
Appendix 4: Example of how the Backpropagation Algorithm Works ...................................................................... 267 
Appendix 5: Example of Hybrid Learning of the ANFIS System .............................................................................. 269 
Appendix 6: GVAI Software Operating Manual ........................................................................................................ 272 
 
ABSTRACT ............................................................................................................................................................. 286 
 
 
 
 
 
LIST OF FIGURES 
Figure 2.1: Branches of the AI field .............................................................................................................................. 23 
Figure 2.2: Mineral systems approach flow diagram .................................................................................................. 26 
Figure 2.3 : Petroleum systems approach flow diagram ............................................................................................. 28 
Figure 3.1: Developed groundwater vulnerability approach flow diagram .............................................................. 31 
Figure 3.2: Schematic illustration of the parameters which make up the proposed groundwater vulnerability 
approach ................................................................................................................................................. 32 
Figure 3.3: Decreasing mean measured and least-squares mean final infiltration rates with increasing slope angle 
(error bars are ± 1 standard error) ...................................................................................................... 34 
Figure 3.4: Relationship between percentage slope and slope angle .......................................................................... 34 
Figure 3.5: Overland flow velocity increases with slope angle (error bars are ± 1 standard error) ........................ 34 
Figure 3.6: Schematic illustration of the parameters used to calculate topographic slope ...................................... 35 
Figure 3.7: Location of the study area in relation to provincial and international boundaries ............................... 41 
Figure 3.8: Climatic data for the Ermelo station showing temperature and rainfall distribution throughout the 
year .......................................................................................................................................................... 43 
Figure 3.9: Extent of the Karoo basin in South Africa, with coalfields. The blue line indicates the location of the 
cross-section AB shown in Figure 3.10 ................................................................................................. 44 
Figure 3.10: Schematic north–south section across the main Karoo basin ............................................................... 45 
Figure 3.11: Local geology of the study area mapped at a 1:250 000 scale showing borehole locations ................. 46 
Figure 3.12: Rock exposure of the granites found in the study area .......................................................................... 47 
Figure 3.13: Malmani Subgroup dolomite rock exposed in the study area displaying an elephant skin texture ... 48 
Figure 3.14: Pretoria Group mudrock outcrop showing heavy fracturing and bedding planes.............................. 48 
Figure 3.15: Weathered sandstone outcrop in the Witbank coalfield ........................................................................ 49 
Figure 3.16: Hydrogeological setting of the study area ............................................................................................... 53 
Figure 3.17: Conceptual model of a karst aquifer ....................................................................................................... 54 
Figure 3.18: Locations of groundwater samples used in this study ............................................................................ 56 
Figure 3.19: Piper diagram showing the major water classifications in relation to the TDS concentration .......... 57 
Figure 3.20: Scatter plot of TDS against sulphate concentration ............................................................................... 58 
Figure 3.21: AMD surface flow from a coal mining operation south of Carolina in the Ermelo coalfield. The 
brownish-orange colour is attributed to iron hydroxyl precipitation ............................................... 60 
Figure 3.22: Elevation image of the study area showing the drainage pattern and rivers ....................................... 61 
Figure 3.23: Topographic slope image of the study area ............................................................................................. 62 
 
 
 
Figure 3.24: Average long-term rainfall of the study area .......................................................................................... 63 
Figure 3.25: Recharge image of the study area ............................................................................................................ 64 
Figure 3.26: Relationship between average long-term rainfall and net recharge ..................................................... 65 
Figure 3.27: Spectral signatures of iron-bearing minerals extracted from the USGS spectral library .................. 68 
Figure 3.28: Secondary iron minerals spectrum resampled to Landsat 8 bandwidths ............................................ 68 
Figure 3.29: Secondary iron minerals spectrum resampled to Sentinel 2 bandwidths ............................................. 69 
Figure 3.30: Decision tree used to identify secondary Fe minerals from Landsat 8 data ......................................... 70 
Figure 3.31: Decision tree used to identify secondary Fe minerals from Sentinel 2 data ......................................... 70 
Figure 3.32: AMD surface sources as interpreted from Landsat 8 remote sensing data.......................................... 72 
Figure 3.33: AMD surface sources as interpreted from Sentinel 2 remote sensing data .......................................... 73 
Figure 3.34: Combined results from Landsat 8 and Sentinel 2 results plotted as a function of distance from 
interpreted AMD surface sources. The areas within the two black polygons are selected for detailed 
analysis .................................................................................................................................................... 74 
Figure 3.35: Zoomed-in results (a) Iron-bearing minerals: (b) Landsat 8 band combination 764 for a detailed 
analysis of interpreted secondary Fe minerals .................................................................................... 75 
Figure 3.36: Zoomed-in results for Arnot North discard mine dump ........................................................................ 76 
Figure 3.37: Subsurface AMD sources as interpreted from geology data ................................................................. 77 
Figure 3.38: Soil types found in the study area ............................................................................................................ 78 
Figure 3.39: Distribution of soil clay content within the study area showing the locations of soil samples collected 
for the chemical traps experiment ........................................................................................................ 79 
Figure 3.40: Experimental setup for determining the attenuation effect of soils on AMD pollution ...................... 81 
Figure 3.41: Soil CEC map of the study area ............................................................................................................... 82 
Figure 3.42: Scatter plot between soil CEC and soil clay content .............................................................................. 83 
Figure 3.43: XRF Mineralogical composition of the soil samples ............................................................................... 83 
Figure 3.44: Plot of soil clay content against iron (Fe) leachate concentration. The red line marks the initial Fe 
concentration of the AMD. The blue and black points are leachate concentration values resulting 
from the effect of adding de-ionised water and AMD to soils respectively ....................................... 84 
Figure 3.45: Plot of soil clay content against Aluminium (Al) leachate concentration. The red line marks the initial 
Fe concentration of the AMD and the blue and black points are leachate concentration values 
resulting from the effect of adding de-ionised water and AMD to soils respectively ....................... 85 
Figure 3.46: Plot of soil clay content against Sulphate (SO -24 ) leachate concentration ............................................. 86 
Figure 3.47: Plot of soil clay content against leachate Calcium (Ca) concentration ................................................. 86 
Figure 3.48: Plot of soil clay content against leachate Magnesium (Mg) concentration ........................................... 87 
Figure 3.49: Plot of soil clay content against leachate Sodium (Na) concentration .................................................. 87 
 
 
 
Figure 3.50: Residual magnetic field with lineaments and interpretations of the faults .......................................... 89 
Figure 3.51: Magnetic analytical signal showing the interpretation of the sills ........................................................ 90 
Figure 3.52: Magnetic interpretation of the possible preferential pathways ............................................................. 91 
Figure 3.53: Possible regional preferential pathways for AMD represented as a distance map ............................. 92 
Figure 3.54: Rock permeability map generated from the literature, reflecting the values of the rocks found in the 
study area. Values in brackets are in cm2 ............................................................................................ 93 
Figure 3.55: Aquifer hydraulic conductivity map of the study area .......................................................................... 94 
Figure 3.56: Depth to water level map derived from monitoring borehole information from the Department of 
Water and Sanitation ............................................................................................................................. 95 
Figure 3.57: Schematic laboratory setup for (a) saturated and (b) unsaturated column tests ................................ 97 
Figure 3.58: Experimental setup for determining the attenuation effect of vadose zone and in the aquifer system. 
The yellow section was replaced by AMD collected from the field .................................................... 98 
Figure 3.59: Mineral composition of various rocks as measured by XRD, showing the five selected samples for the 
column leach experiment ....................................................................................................................... 99 
Figure 3.60: XRF minerals composition of various rocks showing the five selected for the column leach experiment
 ................................................................................................................................................................. 99 
Figure 3.61: Microscopic view of the medium to coarse-grained diabase showing elongated crystals of plagioclase 
feldspar (Sample WITS1) .................................................................................................................... 100 
Figure 3.62: Quartzitic sandstone with lithic fragments as seen under the microscope for sample WITS7 ........ 101 
Figure 3.63: Very fine grains of quartz and feldspar as seen under the microscope for sample WITS8 .............. 101 
Figure 3.64: Plagioclase laths ophitically to sub-ophitically enclosed in clinopyroxene, as seen under the microscope 
for sample WITS9 ................................................................................................................................ 102 
Figure 3.65: Very fine-grained calcite and dolomite predominate in sample WITS14, as seen under the microscope
 ............................................................................................................................................................... 102 
Figure 3.66: Graphic plot of leachate pH against time for various rocks under saturated conditions ................. 103 
Figure 3.67: Graphic plot of leachate pH with time for various rocks under unsaturated conditions ................. 104 
Figure 3.68: Graphic plot of leachate EC with time for various rocks under saturated conditions ...................... 105 
Figure 3.69: Graphic plots of leachate EC with time for various rocks under unsaturated conditions ................ 105 
Figure 3.70: Graphic plot of leachate sulphate concentrations over time for various rocks under saturated 
conditions .............................................................................................................................................. 106 
Figure 3.71: Graphic plot of leachate sulphate concentration over time for various rocks under unsaturated 
conditions .............................................................................................................................................. 106 
Figure 3.72: Graphic plot of leachate iron concentrations over time for various rocks under saturated conditions
 ............................................................................................................................................................... 107 
 
 
 
Figure 3.73: Graphic plot of leachate iron concentration over time for various samples under unsaturated 
conditions .............................................................................................................................................. 107 
Figure 3.74: Graphic plot of leachate aluminium concentrations over time under saturated conditions ............. 107 
Figure 3.75: Graphic plot of leachate aluminium concentration over time for various samples under unsaturated 
conditions .............................................................................................................................................. 108 
Figure 3.76: Graphic plot of leachate manganese concentrations over time for various samples under saturated 
conditions .............................................................................................................................................. 108 
Figure 3.77: Graphic plot of leachate manganese concentrations over time for various samples under unsaturated 
conditions .............................................................................................................................................. 109 
Figure 3.78: Graphic plot of leachate magnesium concentrations over time for various samples under saturated 
conditions .............................................................................................................................................. 109 
Figure 3.79: Graphic plot of leachate magnesium concentrations over time for various samples under unsaturated 
conditions .............................................................................................................................................. 110 
Figure 3.80: Graphic plot of leachate sodium concentrations over time for various samples under saturated 
conditions .............................................................................................................................................. 110 
Figure 3.81: Graphic plot of leachate sodium concentrations over time for various samples under unsaturated 
conditions .............................................................................................................................................. 111 
Figure 3.82: Graphic plot of leachate calcium concentrations over time for various samples under saturated 
conditions .............................................................................................................................................. 111 
Figure 3.83: Graphic plot of leachate calcium concentrations over time for various samples under unsaturated 
conditions .............................................................................................................................................. 111 
Figure 3.84: Graphic plot of leachate chloride concentrations over time for various samples under saturated 
conditions .............................................................................................................................................. 112 
Figure 3.85: Graphic plot of leachate chloride concentrations over time for various samples under unsaturated 
conditions .............................................................................................................................................. 112 
Figure 3.86: Rock-AMD reactivity map of the study area showing the relative classification in terms of extraction 
of AMD pollutants................................................................................................................................ 116 
Figure 4.1: Structure of the fuzzy expert system ....................................................................................................... 119 
Figure 4.2: Crisp to fuzzy translation for (a) sources factor, (b) transportation pathway factor, (c) traps ......... 126 
Figure 4.3: Sources of energy in fuzzy space .............................................................................................................. 129 
Figure 4.4: Sources of ligand (water) in fuzzy space.................................................................................................. 130 
Figure 4.5: Surface sources of AMD pollution in fuzzy space .................................................................................. 131 
Figure 4.6: Subsurface sources of AMD pollution in fuzzy space ............................................................................ 132 
Figure 4.7: All sources of AMD pollution in fuzzy space constituted by combining surface and subsurface sources
 ............................................................................................................................................................... 133 
 
 
 
Figure 4.8: Sources factor produced by integration energy, ligand (water) and pollution sources ....................... 134 
Figure 4.9: Transportation pathways in soils (clay content) expressed in fuzzy values ......................................... 135 
Figure 4.10: Preferential pathways expressed in fuzzy values .................................................................................. 136 
Figure 4.11: Rock permeability expressed in fuzzy values ........................................................................................ 137 
Figure 4.12: Aquifer hydraulic conductivity expressed in fuzzy values ................................................................... 138 
Figure 4.13: Transportation pathways factor generated by combining AMD transport parameters in the soil, 
vadose zone and the aquifer system .................................................................................................... 139 
Figure 4.14: Rock-AMD reactivity expressed in fuzzy values .................................................................................. 140 
Figure 4.15: Depth to water table expressed in fuzzy values .................................................................................... 141 
Figure 4.16: Traps factor generated by combining natural AMD trapping parameters in the soil, vadose zone and 
the aquifer system ................................................................................................................................ 142 
Figure 4.17: Multistage fuzzy inference network used for combining input layers to produce the groundwater 
vulnerability model .............................................................................................................................. 143 
Figure 4.18: Resultant groundwater vulnerability model of the Witbank, Ermelo and Highveld coalfields ....... 144 
Figure 4.19: Aerial size distribution of various groundwater vulnerability classes ................................................ 145 
Figure 4.20: Correlation scatter plots for sulphate against groundwater vulnerability model values .................. 146 
Figure 4.21: Sulphate concentration map generated from the NGA database........................................................ 147 
Figure 4.22: Profile along cross-section A–B showing the DWS borehole sulphate concentrations and the fuzzy 
vulnerability model profile .................................................................................................................. 148 
Figure 4.23: Simple layout of conventional four-electrode array used to measure the subsurface resistivity...... 149 
Figure 4.24: Simple layout of conventional seismic refraction survey ..................................................................... 151 
Figure 4.25: 2D resistivity survey results for site 1 showing (a) the modelled apparent resistivity-elevation, (b) the 
derived porosity-elevation and (c) seismic velocity plot .................................................................... 152 
Figure 4.26: 2D resistivity survey results for site 2 showing (a) the modelled apparent resistivity-elevation plot, (b) 
the derived porosity-elevation plot and (c) the seismic velocity plot ............................................... 153 
Figure 4.27: 2D resistivity survey results for site 3 showing (a) the modelled apparent resistivity-elevation plot, (b) 
the derived porosity-elevation plot and (c) the seismic velocity plot ............................................... 155 
Figure 4.28: Black clay layer observed overlying the weathered sandstone at an excavated trench next to the 
surveyed site 3 ...................................................................................................................................... 155 
Figure 4.29: 2D resistivity survey results for site 4 showing (a) the modelled apparent resistivity-elevation, (b) the 
derived porosity-elevation and (c) the seismic plots .......................................................................... 157 
Figure 5.1: Spatial association test results for the rainfall parameter ..................................................................... 163 
Figure 5.2: Rainfall map layer in binary format ........................................................................................................ 164 
Figure 5.3: Spatial association test results for the slope parameter ......................................................................... 165 
 
 
 
Figure 5.4: Slope map layer in binary format ............................................................................................................ 165 
Figure 5.5: Spatial association test results for surface sources parameter .............................................................. 166 
Figure 5.6: Surface sources map layer in binary format ........................................................................................... 167 
Figure 5.7: Spatial association test results for the subsurface sources parameter .................................................. 167 
Figure 5.8: Subsurface sources map layer in binary format ..................................................................................... 168 
Figure 5.9: Spatial association test results for the soil clay parameter .................................................................... 169 
Figure 5.10: Soil clay map layer in binary format ..................................................................................................... 169 
Figure 5.11: Spatial association test results for the pathway parameter ................................................................. 170 
Figure 5.12: Pathway map layer in binary format .................................................................................................... 170 
Figure 5.13: Spatial association test results for the relative aquifer hydraulic conductivity ................................. 171 
Figure 5.14: Relative aquifer hydraulic conductivity map layer in binary format ................................................. 171 
Figure 5.15: Spatial association test results for the relative rock permeability parameter .................................... 172 
Figure 5.16: Relative rock permeability map layer in binary format ...................................................................... 173 
Figure 5.17: Spatial association test results for the rock-AMD reactivity parameter ............................................ 174 
Figure 5.18: Rock-AMD reactivity map layer in binary format............................................................................... 174 
Figure 5.19: Spatial association test results for the depth to water table parameter .............................................. 175 
Figure 5.20: Depth to water table map layer in binary format ................................................................................. 175 
Figure 6.1: Simplified illustration of a biological neuron .......................................................................................... 181 
Figure 6.2: Working principle of an artificial neuron ............................................................................................... 182 
Figure 6.3: Activation functions commonly used in artificial neural networks: (a) binary (b) sigmoid and (c) 
hyperbolic tangent ............................................................................................................................... 184 
Figure 6.4: Artificial neural network architecture defined by the way in which neurons (yellow, green and blue 
blobs) are connected by synapses (lines) ............................................................................................ 186 
Figure 6.5: Testing errors at various training epochs ............................................................................................... 193 
Figure 6.6: Testing errors at various number of neurons in the hidden layer ........................................................ 194 
Figure 6.7: ANN architecture used for training ......................................................................................................... 195 
Figure 6.8: Graph for determining the best fold with the lowest validation error ................................................. 196 
Figure 6.9: Groundwater vulnerability model of the Witbank, Ermelo and Highveld coalfields generated by using 
ANNs ..................................................................................................................................................... 197 
Figure 6.10: Aerial size distribution of various groundwater vulnerability classes ................................................ 198 
Figure 6.11: Correlation scatter plots for sulphate against groundwater vulnerability model values .................. 199 
Figure 6.12: Profile along cross-section A–B showing the DWS borehole sulphate concentration and the ANN 
vulnerability model profile .................................................................................................................. 200 
 
 
 
Figure 7.1: Neural-fuzzy system .................................................................................................................................. 204 
Figure 7.2: Fuzzy neural system .................................................................................................................................. 205 
Figure 7.3: First-order Sugeno ANFIS architecture .................................................................................................. 207 
Figure 7.4: Membership functions used for the ANFIS system for a groundwater vulnerability assessment ..... 213 
Figure 7.5: Determining the cut-off epoch value for training the ANFIS system ................................................... 214 
Figure 7.6: ANFIS groundwater vulnerability model of the Witbank, Ermelo and Highveld coalfields .............. 215 
Figure 7.7: Aerial size distribution of the various groundwater vulnerability classes ........................................... 216 
Figure 7.8: Correlation scatter plots for sulphate against the ANFIS groundwater vulnerability model ............ 217 
Figure 7.9: Profile along cross-section A–B showing the DWS borehole sulphate concentrations and the ANFIS 
vulnerability model profile .................................................................................................................. 218 
Figure 8.1: Systems design flowchart of the groundwater vulnerability (GVAI) toolbox ...................................... 222 
Figure 8.2: Main menu module window ..................................................................................................................... 223 
Figure 8.3: Input module window ............................................................................................................................... 224 
Figure 8.4: The “about” window, showing the software details ............................................................................... 224 
Figure 8.5: Fuzzy expert system flow chart ................................................................................................................ 225 
Figure 8.6: Fuzzy expert system module window ...................................................................................................... 226 
Figure 8.7: Data-driven artificial intelligence data pre-processing module window .............................................. 227 
Figure 8.8: ANN system flow chart showing the relationships of various algorithms ............................................ 228 
Figure 8.9: ANN module window ................................................................................................................................ 229 
Figure 8.10: ANFIS expert system flow chart ............................................................................................................ 230 
Figure 8.11: ANFIS module window ........................................................................................................................... 231 
Figure 8.12: Model validation module ........................................................................................................................ 232 
Figure A1: Determining the optimum number of epochs with minimum testing MSE.......................................... 256 
Figure A2: Determining the optimum number of neurons in hidden layer with minimum testing MSE ............. 257 
Figure A3: Illustration of three way data splitting .................................................................................................... 258 
Figure A4: Holdout method splitting the dataset into training, validation and testing sets ................................... 259 
Figure A5: Random subsampling and splitting of the dataset into training, validation and testing sets .............. 260 
Figure A6: K-fold cross-validation splitting of the dataset into training, validation and testing .......................... 261 
Figure A7: Leave-one-out cross-validation splitting of the dataset into training, validation and testing ............. 262 
Figure A8: Leave-one-out cross-validation graph ..................................................................................................... 263 
Figure A9: Example of how the back propagation algorithm works ....................................................................... 264 
Figure A10: Plot of fuzzy membership function for each of the rules...................................................................... 267 
 
 
 
Figure A11: Example of calculations and layer connections for layers 1, 2 and 3 .................................................. 267 
Figure A12: Example of calculations and layer connections for layers 4 and 5 ...................................................... 268 
Figure A13: GVAI launch module .............................................................................................................................. 270 
Figure A14: Input module window ............................................................................................................................. 272 
Figure A15: About window .......................................................................................................................................... 273 
Figure A16: Input module window ............................................................................................................................. 273 
Figure A17: Input module window ............................................................................................................................. 274 
Figure A18: Fuzzy expert system module window..................................................................................................... 275 
Figure A19: Source output in fuzzy values ................................................................................................................. 276 
Figure A20: Map output after combining all the inputs from the sources .............................................................. 276 
Figure A21: Fuzzy expert system output map ............................................................................................................ 277 
Figure A22: Data-driven artificial intelligence data pre-processing module window ............................................ 278 
Figure A23: Spatial association test result .................................................................................................................. 278 
Figure A24: ANN module window .............................................................................................................................. 279 
Figure A25: Display of ANN results ............................................................................................................................ 279 
Figure A26: Adaptive Neural-Fuzzy Inference System module window ................................................................. 280 
Figure A27: Adaptive Neural-Fuzzy Inference module ............................................................................................ 281 
Figure A28: Model comparison module ..................................................................................................................... 282 
Figure A29: Validation graph of the fuzzy model ...................................................................................................... 282 
  
 
 
 
LIST OF TABLES 
Table 2.1: Original DRASTIC parameters (Aller et al., 1987) ................................................................................... 13 
Table 2.2: Original GOD parameters (Gogu and Dassargues, 2000) ......................................................................... 15 
Table 2.3: Vulnerability classes of the AVI method (Fraga et al., 2013) .................................................................... 17 
Table 2.4: Brief history of Artificial Intelligence ......................................................................................................... 22 
Table 2.5: Interpretation of the R value (Arikunto, 2002) .......................................................................................... 25 
Table 3.1: Summary of the geology of the Witbank, Ermelo and Highveld coalfields ............................................. 50 
Table 3.2: Properties of Landsat 8 data (Cole et al., 2015) .......................................................................................... 67 
Table 3.3: Properties of Sentinel 2 (Satellite Imaging Corporation., 2017) ............................................................... 67 
Table 3.4: Soil types found in the study area and their associated estimated clay content ...................................... 79 
Table 3.5: Chemical composition of AMD used for the soil batch leach experiment ............................................... 81 
Table 3.6: CEC, pH and clay content of the soil samples used in the batch leach experiment ................................ 82 
Table 3.7: Groups of samples according to their mineral speciation as interpreted from XRF results ................ 100 
Table 3.8: Summary of rock–AMD reactivity expressed in terms of AMD removal by rocks .............................. 114 
Table 3.9: Summary of the rock-AMD reactivity for the Witbank, Ermelo and Highveld coalfields ................... 115 
Table 4.1: Assigning map weights, class weights and confidence factors for various layers .................................. 125 
Table 4.2: Aerial coverage of various vulnerability classes ....................................................................................... 145 
Table 4.3: Comparison of derived porosity values and groundwater vulnerability model values for each of the 
survey sites ............................................................................................................................................ 158 
Table 5.1: Relationships of parameters used for the calculation of spatial association .......................................... 162 
Table 5.2: Assignment of binary classes ..................................................................................................................... 176 
Table 6.1: Aerial coverage of various vulnerability classes ....................................................................................... 197 
Table 6.2: Comparison of derived porosity values and the ANN groundwater vulnerability model values for each 
of the survey sites ................................................................................................................................. 201 
Table 7.1: Passes in the hybrid learning algorithm (Jang and Sun, 1995) ............................................................... 209 
Table 7.2: Aerial coverage of various vulnerability classes of the ANFIS model .................................................... 216 
Table 7.3: Comparison of derived porosity values and ANFIS groundwater vulnerability model values for each of 
the survey sites ..................................................................................................................................... 219 
Table 9.1: Recommendations for the management of the water resources of the Witbank, Ermelo and Highveld 
coalfields ............................................................................................................................................... 238 
Table A2: Example of a dataset with four points for running the leave-one-out cross-validation technique ....... 263 
Table A3: Data splitting of a four points example using the leave-one-out algorithm ........................................... 263 
 
 
 
LIST OF ACRONYMS 
KZN  –  KwaZulu-Natal 
MKB   –  Main Karoo Basin 
RBCT   –  Richards Bay Coal Terminal 
AI   –  Artificial Intelligence 
AMD   –  Acid Mine Drainage 
ANFIS  –  Adaptive Neural-Fuzzy Inference System 
ANN   –  Artificial Neural Network 
ARC- ISCW  –  Agricultural Research Council Institute of Soil, Climate and Water 
ASI   –  Italian Space Agency 
AVI  –  Aquifer Vulnerability Index 
CEC   –  Cation Exchange Capacity 
CMB   –  Chloride Mass Balance 
DLR  –  German Aerospace Centre 
DN  – Digital Number 
DRASTIC – Depth to water table, net Recharge, Aquifer media, Soil media, Topographic                         
s                                  slope, Impact of vadose zone, hydraulic Conductivity 
DWS  – Department of Water and Sanitation 
EC  – Electrical Conductivity 
ERT   – Electrical Resistivity Tomography 
ESKOM – Electricity Supply Commission 
FMF  – Fuzzy Membership Function 
FMV  – Fuzzy Membership Value 
GARIC – Generalised Approximate Reasoning-based Intelligent Control 
GIS  – Geographic Information System 
GOD  – Groundwater occurrence, Overall lithology, Depth to water table 
GPS  – Global Positioning System 
i 
 
 
GUI  – Graphic User Interface 
GVAI  – Groundwater Vulnerability Artificial Intelligence 
IC  – Ion Chromatography 
ICP-MS – Inductively Coupled Plasma Mass Spectrometry 
LISP  – Locator/Identifier Separation Protocol 
LSM  – Least Squares Method 
MSE  – Mean Square of Errors 
MTEF  – Medium Term Expenditure Framework 
NASA  – National Aeronautics and Space Administration 
NGA  – National Groundwater Archive 
NGIA  – National Geospatial Intelligence Agency 
NIR  – Near-Infra-Red 
NNDFR – Neural Network Driven Fuzzy Reasoning 
NP  – Non-Polluted 
P  – Polluted 
pH  – potential Hydrogen 
SACS  – South African Committee for Stratigraphy 
SAWS  – South African Weather Services 
SCMAI – Supervised Committee Machine Artificial Intelligence 
SIINTACS – Soggiacenza, Infiltrazione efficace, Non saturo, Tipologia della copertura, 
   Acquifero, Conducibilita idraulica, Supeficia topografica 
SPT  – Sources, transportation Pathway, Traps 
SRTM  – Shuttle Radar Topographic Mission 
STA  – Source, Transport, Attenuation 
SWIR  – Short-Wave Infra-Red 
T and DB – Transvaal and Delagoa Bay 
TDS  – Total Dissolved Solids 
TIR  – Thermal Infra-Red 
ii 
 
 
USEPA – United States Environmental Potential Agency 
USGS  – United States Geological Survey 
VNIR  – Visible and Near-Infra-Red 
WSI  – Weighted Sum of Inputs 
XRD  – X-Ray Diffraction 
XRF  – X-Ray Fluorescence 
iii 
 
 
MEASUREMENT UNITS 
%   - percentage 
km   - kilometre 
km2  - square kilometre 
mm   - millimetre 
m   - metre 
ha   - hectare 
Mt   - million tonnes 
Bt   - billion tonnes 
p.a.   - per annum 
m/s   - metre per second 
m/d   - metre per day 
yr   - year 
mg/L   - milligram per litre 
o  - degree 
mm/h  - millimetre per hour 
cm/s  - centimetre per second 
mm/a   - millimetre per annum 
µm  - micro metre 
nT   - nanoTesla 
nT/m  - nanoTesla per metre 
mS/m  - milliSiemens per metre 
cmol/kg  - centimoles per kilogram 
gpd/ft2  - gallons per day per square foot 
  
iv 
 
 
OUTCOMES OF THE RESEARCH 
Sakala, E., Fourie, F., Gomo, M. and Coetzee, H. 2018. GIS-based groundwater vulnerability 
modelling: a case study of the Witbank, Ermelo and Highveld coalfields in South Africa, 
Journal of African Earth Sciences, 137, 46–60. doi: 10.1016/j.jafrearsci.2017.09.012. 
Sakala, E., Fourie, F., Gomo, M. and Coetzee, H. 2017a. Hydrogeological investigation of the 
Witbank , Ermelo and Highveld coalfields : implications for the subsurface transport and 
attenuation of acid mine drainage, in Wolkersdorfer, C., Sartz, L., Sillanpää, M., and 
Häkkinen, A. (eds) 13th International Mine Water Association Congress – Mine Water & 
Circular Economy. Lappeenranta, Finland: IMWA, 564–571. 
Sakala, E., Fourie, F., Gomo, M. and Coetzee, H. 2017b. Mapping surface sources of acid mine 
drainage using remote sensing: case study of the Witbank , Ermelo and Highveld coalfields, 
in Wolkersdorfer, C., Sartz, L., Sillanpää, M., and Häkkinen, A. (eds) 13th International Mine 
Water Association Congress – Mine Water & Circular Economy. Lappeenranta, Finland: 
IMWA, 1246–1253. 
Sakala, E., Fourie, F., Gomo, M., Coetzee, H. and Magadaza, L. 2016. Specific groundwater 
vulnerability mapping: case study of acid mine drainage in the Witbank coalfield, South 
Africa, in 6th IASTED International Conference on Environment and Water Resource 
Management, 93–100. doi: 10.2316/P.2016.836-010. 
  
v 
 
 
CHAPTER 1: INTRODUCTION 
1.1 BACKGROUND 
Globally, groundwater is an important and most valuable source of water for various purposes 
(consumption, irrigation, industry and mining, etc.) owing to its relatively low susceptibility to 
pollution and relative abundance. However, the resource is under serious threat by human activities 
that introduce pollutants or group of pollutants on surface or in the subsurface (e.g. mining, industrial, 
agricultural and waste disposal). Once a groundwater system is polluted it is often costly and 
technically challenging to restore, and can be practically impossible to remediate in some instances 
(Thirumalaivasan et al., 2003; Kaur and Rosin, 2009). Thus, it is important to identify the 
groundwater systems and geo-environmental settings which are most vulnerable to pollution. This 
necessity has prompted researchers, government agencies and environmentalists to devise ways of 
addressing groundwater pollution issues. 
Several methodologies have been developed since the 1980s to predict the consequences of a 
pollutant or group of pollutants entering the groundwater from the surface or near surface through 
human activities (Aller et al., 1987; Van Stempvoort et al., 1993; Civita, 1994). That is, investigations 
are conducted to identify areas that are more likely than others to become polluted, leading to the 
usage of the phrase “groundwater vulnerability to pollution” (NRC, 1993). 
Groundwater vulnerability assessments are undertaken with the overall goal of assessing the relative 
impact with which a given hydrogeology, geology or subsurface can inhibit pollutants from reaching 
the groundwater system. Assessments of groundwater vulnerability are divided in two major types, 
namely the “intrinsic vulnerability assessment” and the “specific vulnerability assessment” (NRC, 
1993). The intrinsic type defines only the ease with which a pollutant or a group of pollutants migrates 
from the surface to the groundwater (Aller et al., 1987). The specific type, in turn, takes into 
consideration the properties of the pollutant and its interaction with the subsurface (Vrba and 
Zoporozec, 1994; Huan et al., 2012). According to Huan et al. (2012), nowadays, the impact of 
intrinsic vulnerability is negligible when compared to specific vulnerability because factors that affect 
intrinsic vulnerability, such as depth to the water table, soil and recharge are constantly subject to the 
influences of human intervention. Hence, most assessments are formulated for a specific pollutant or 
group of pollutants or certain human activities which have an impact on the groundwater 
environment. Groundwater vulnerability results are a very useful tool for advising policy and decision 
makers on the vulnerability of groundwater systems which may be incorporated into groundwater 
management programmes and are thus instrumental in the protection of groundwater. 
1 
 
 
It should be noted that groundwater vulnerability assessments are a general planning and decision-
making tool rather than a scientifically precise protocol for predicting future pollution. They are used 
to assess the general likelihood of pollution occurring in groundwater. According to the NRC (1993), 
a specific limitation of groundwater vulnerability assessments is that all groundwater is vulnerable to 
some degree. Furthermore, uncertainty and subjectivity are inherent in most vulnerability assessments 
as these assessments rely on expert opinions. These limitations have to be taken into consideration 
when formulating groundwater vulnerability assessments, especially if the results are intended to be 
used for critical applications such as policy and decision-making. 
In order to reduce the subjective nature of assessment approaches and to reduce the uncertainty in 
groundwater vulnerability data processing, Artificial Intelligence (AI) systems, which have been 
successfully used in fields such as robotics, science and engineering, can be utilised (PWC, 2017). 
Artificial intelligence is the study of how to make computers do things, which at the moment are 
better accomplished by people, such as perception, learning, reasoning and action (Rich and Knight, 
1991; Russell and Norvig, 1995; Negnevitsky, 2005). The benefits of using AI for data processing 
and the automation of some processes is that while human minds can only consider a limited number 
of variables at a time and are prone to subjective bias, AI programmed computers can process much 
larger amounts of information at much faster speeds with great accuracy. Therefore, groundwater 
vulnerability assessments can be greatly improved in terms of speed, reliability and consistency while 
reducing human induced uncertainties by incorporating AI systems that can imitate human cognitive 
and learning processes (Fijani et al., 2013; Porwal and Carranza, 2015). 
Groundwater vulnerability assessments were originally formulated and widely used for pollution 
from agricultural pesticides (Aller et al., 1987; Secunda et al., 1998; Huan et al., 2012; Sorichetta et 
al., 2012; Boufekane and Saighi, 2013; Jang and Chen, 2015; Kazakis and Voudouris, 2015; Pisciotta 
et al., 2015) and to investigate municipality pollutant sources (Somaratne et al., 2013). In the 
literature, there are a few groundwater vulnerability assessment case studies on mining activities as a 
source of pollution, specifically coal mining (Atanacković et al., 2016; Ewusi et al., 2017; Haque et 
al., 2018). Yet, coal is one of the cornerstones of economic development and is a vital contributor to 
the industrial development of many developed and developing countries, such as China, the United 
States of America, India, South Africa, Zimbabwe and Mozambique (World Coal Association, 2012; 
Statistics South Africa, 2016). 
Globally, coal is currently the most widely used primary fuel, accounting for approximately 40% of 
the world's electricity production (World Coal Association, 2012; Eskom, 2016). The call to decrease 
the world’s dependence on coal as an energy source is purposeful where lowering its use reduces 
2 
 
 
greenhouse gas emissions and lowers the environmental impacts associated with coal mining (World 
Coal Association, 2012; Statistics South Africa, 2016). However, for countries that are heavily 
dependent on coal, a migration to more environmentally friendly sources of energy would take a long 
time owing to a number of social and economic factors such as the significant infrastructural 
investment that has already been made in the coal industry and a lack of suitable alternative sources. 
Moreover, coal can currently be exploited at an extremely favourable cost and the industry has offered 
significant employment opportunities (World Coal Association, 2012; Jeffrey et al., 2014; 
Department of Energy, 2016). Considering the benefits of coal coupled with recent global research 
mainly focussed on the mitigation of environmental problems associated with coal mining and its 
utilisation, carbon capture, clean coal technologies and best practice environmental management 
options for coal mining and coal waste disposal, coal may still be fully utilised with minimum or no 
harm to the environment. 
The environmental problems associated with coal mining and coal waste disposal include dust 
fallouts, land subsidence at undermined areas, the appearance of tension cracks at the surface and 
crown-hole development, deterioration of surface and groundwater quality and spoil heaps (Bell et 
al., 2001). The most significant of these is the deterioration of surface and groundwater quality owing 
to mine drainage, particularly Acid Mine Drainage (AMD) (Zaporozec, 1981). AMD occurs when 
sulphide minerals (pyrite and marcasite) associated with the ore and host rock are exposed to 
atmospheric conditions during coal mining operations and are oxidised in the presence of oxygen and 
water. The process is catalysed by iron and sulphur-oxidising bacteria producing an acidic solution 
characterised by low pH values, high concentrations of sulphate and total dissolved solids (TDS). In 
this acidic environment heavy metals such as iron, aluminium and manganese may be remobilised 
resulting in elevated concentrations in the groundwater (U.S Environmental Protection Agency, 1977; 
Bell et al., 2001; Pinetown et al., 2007). Elevated concentrations of these elements in water resources 
(ground and surface water) cause the water quality to deteriorate which may affect aquatic life and 
may pose serious health concerns to humans and animals dependent on the water resource (U.S 
Environmental Protection Agency, 1977). 
In ensuring that coal mining and coal waste disposal can be done without harming the environment, 
policy and decision makers play a vital role. In order to assist policy and decision makers to formulate 
strategies which help in the prevention and remediation of environmental problems, policy and 
decision making processes need to incorporate groundwater vulnerability assessments that support 
land-use planning and regulate mining activities. Groundwater vulnerability assessment 
methodologies range from simple, qualitative and relatively inexpensive approaches to rigorous, 
quantitative, and costly assessments, where trade-offs must be carefully considered among the 
3 
 
 
competing influences of cost, scientific defensibility and the amount of acceptable uncertainty in 
meeting the decision making objectives (Focazio et al., 2002). 
This research involves the development of cost-effective groundwater vulnerability assessment tools 
driven by the power of AI to overcome current challenges faced by many groundwater vulnerability 
techniques. At the same time, the research fills a gap in groundwater vulnerability assessments for 
AMD pollution on a typical coalfield scale. The tools to be developed are anticipated to provide 
scientifically defensible information which can easily be incorporated into a typical water-resource 
management decision-making process for policy and decision-makers, ultimately guiding 
environmental management options for coal mining and coal waste disposal. 
The Witbank, Ermelo and Highveld coalfields in Mpumalanga Province of South Africa are the 
country’s current largest producers of coal. Their coal is of good quality and is suitable for electricity 
generation. The coalfields have vast coal deposits, which are relatively economical to mine (Banks et 
al., 2011). These coalfields have been exploited for over a century and have contributed to the 
economic development of the country by supplying energy to developing industries and to the 
growing urban population of South Africa (McCarthy and Pretorius, 2009). These coalfields supply 
more than 50% of South Africa’s saleable coal and feed the country’s major coal-fired power stations, 
including the Kendal, Duvha, Komati and Arnot Power Stations (Hancox and Götz, 2014). 
However, the coal mining operations in the Highveld, Ermelo and Witbank coalfields have caused 
water quality deterioration of both surface and groundwater resources as a result of AMD and heavy 
metals pollution (Bell et al., 2002; McCarthy and Pretorius, 2009) and pose a serious concern for 
local communities, as well as environmental, mining and water regulatory authorities. Several areas 
have been mined out and some areas are still to be mined. Thus, appropriate tools to avoid and 
mitigate impacts of mining on the groundwater need to be developed. These coalfields will be used 
in the current study to develop and test the rapid groundwater vulnerability assessment tools for policy 
and decision makers, specifically dealing with AMD pollution at a coalfield scale. 
When the title of the PhD thesis was registered, the research aimed at using only Witbank and 
Ermelo coalfields as units of study but the scope was increased to cover Highveld coalfield as a 
bonus as it is located adjacent to these coalfields.  
1.2 AIMS AND OBJECTIVES 
This research is part of a broader Mine Water Management Project undertaken by the Council for 
Geoscience, funded under the Medium Term Expenditure Framework (MTEF) by the Department of 
Mineral Resources (DMR) of South Africa. The overall goal of the Mine Water Management Project 
4 
 
 
is to generate proactive environmental management strategies dealing specifically with the 
management of mine water in the coalfields and goldfields of South Africa. The main aim of this 
research is to develop scientifically defensible groundwater vulnerability assessment tools for use by 
policy and decision makers in controlling coal mining and coal waste disposal in a typical coalfield 
using the Witbank, Ermelo and Highveld coalfields of South Africa as case studies. 
The objectives for the research are: 
• To critically analyse available groundwater vulnerability approaches and AMD pollution to 
develop a specific approach applicable to a typical coalfield. 
• To incorporate AI in the form of expert systems and machine learning (adaptive learning) 
algorithms in order to enhance the human capabilities in the assessment of groundwater 
vulnerability, specifically to coalfields. 
• To perform laboratory and field experiments and to analyse results in view of selecting 
appropriate groundwater vulnerability input map layers and validating vulnerability models. 
• To develop a simple-to-use graphic user interface toolbox from where the rapid assessment 
tools for groundwater vulnerability of a typical coalfield can be used. 
1.3 OUTLINE OF RESEARCH METHODOLOGY 
To achieve the research aim and objectives, the following research methodology was applied: 
1. A review of relevant publications (journals, books, theses and websites) dealing with AMD, 
groundwater vulnerability assessments, coal mining and waste disposal, AI and regional 
assessment tools was undertaken. 
2. Globally accepted and well-structured frameworks for regional spatial data assessments 
(mineral systems and petroleum approaches) were translated into a standardised holistic 
approach for the assessment of groundwater vulnerability to AMD pollution. 
3. The developed approach was applied to the largest coal producing coalfields of South Africa, 
in particular the Witbank, Ermelo and Highveld coalfields. 
4. A knowledge-driven, data-driven and hybrid AI system was developed and tested to assess its 
applicability in obviating shortcomings inherent to currently used approaches to evaluating 
groundwater vulnerability. 
5. Using the Witbank, Ermelo and Highveld coalfields as the unit of study, the following 
experiments and studies were carried out: 
5 
 
 
• Laboratory column leachate experiments (both for saturated and unsaturated conditions) 
were carried out to observe and rank various rocks in terms of their neutralising potential 
and to determine which rock formations are able to extract pollutants from AMD. 
• Mineralogical studies of rocks using x-ray florescence (XRF), x-ray diffraction (XRD) 
and petrography were undertaken to aid in the interpretation of the rock-AMD reactivity 
experiment. 
• A soil batch leach experiment was used to study AMD pollution in the soils. 
• Hydrogeological studies were conducted to understand the transport of AMD in the 
vadose zone and the aquifer system. 
• The results of the above studies were combined with other datasets to produce 
groundwater vulnerability models for the three coalfields. The results were validated by 
statistical and hydro-geochemical methods. 
1.4 LIMITATIONS OF THE RESEARCH 
Groundwater vulnerability assessments are inherently scale dependent, ranging from local to large — 
that is, from a point location to a catchment or coalfield scale. The present research mainly focussed 
on developing groundwater vulnerability assessment tools intended for general land-use planning and 
water resource management and mining regulatory purposes at a large scale such as over a coalfield 
or catchment area. The results allowed for comparison between areas concerning the likelihood of 
AMD infiltrating the groundwater system when released from the earth’s surface. The results may 
provide general guidelines from which site-specific studies can be done for local scale modelling. 
Drainage emanating from mining activities may be classified according to the drainage pH: acid, 
neutral or alkaline mine drainage types. The present research only focusses on AMD which has been 
identified as a major problem affecting a typical coalfield and which can hinder the full utilisation of 
the coal resources. The acidity remobilises heavy toxic metals in solution, resulting in the 
deterioration of the quality of surface and groundwater resources. 
The approach developed in this research only takes into consideration the vertical movement of 
pollutants which are soluble and move together with the water. Although pollution can diffuse 
laterally, this aspect was not considered in the present research. 
Within a given coalfield, there are a large number of types of AMD point sources, such as opencast 
mines, waste rock dumps, tailings dumps and loading bays. Owing to their distribution over a large 
regional area, they will be considered as a regional nonpoint problem and a regional assessment 
methodology used. 
6 
 
 
 
1.5 STRUCTURE OF THE THESIS 
The thesis is structured as follows: 
• Chapter 1 is an introductory chapter which provides background information leading to the 
formulation of the research. It highlights the general outline of the research and the envisaged 
benefits from such a research to the global drive towards the sustainable utilisation of coal 
resources while ensuring minimum damage to the environment. 
• Chapter 2 discusses the various groundwater vulnerability approaches, their strengths and 
shortcomings with reference to their usage for AMD specific groundwater vulnerability 
assessment and how they can be improved by usage of AI. Globally accepted and well-
structured frameworks (mineral systems, petroleum and source-pathway-receptor approaches) 
are also discussed. 
• Chapter 3 outlines the formulation of a standardised holistic approach SPT for the assessment 
of groundwater vulnerability with regard to AMD. SPT represents the following groundwater 
vulnerability factors: source, transportation pathways and traps. 
• Chapter 4 gives an outline of knowledge-driven artificial intelligence methodologies, in 
particular the fuzzy expert system. The chapter provides a formulation of the fuzzy expert 
system, together with its results and a validation and discussion of the system, as applied to a 
groundwater vulnerability assessment of the Witbank, Ermelo and Highveld coalfields using 
SPT input parameters. 
• Chapter 5 deals with the data preparation steps followed in converting the raw data into a 
format that is accepted by data-driven approaches. A description of the algorithms that are used 
for the autonomous processing of data-driven approaches are given in this chapter. 
• Chapter 6 describes the data-driven artificial intelligence methodology, in particular artificial 
neural networks (ANN). This chapter includes a formulation of the methodology, the results, 
validation and a discussion of the application of the methodology to a groundwater vulnerability 
assessment of the Witbank, Ermelo and Highveld coalfields of South Africa using the SPT input 
parameters. 
• Chapter 7 gives an outline of the hybrid artificial intelligence methodology, in particular of the 
adaptive neuro-fuzzy inference system (ANFIS). A discussion of its formulation, results and 
validation as applied in the context of a groundwater vulnerability assessment of the Witbank, 
Ermelo and Highveld coalfields of South Africa using SPT input parameters is given in this 
chapter. 
7 
 
 
• Chapter 8 deals with a formulation of a software platform (toolbox) for the rapid assessment 
of the AMD-specific groundwater vulnerability of a typical coalfield and a discussion of how 
the platform can be applied in policy and decision-making processes. 
• Chapter 9 provides overall concluding remarks and recommendations based on the findings of 
this research and highlights possible further research areas. 
• The Appendices contain all the data gathered during the course of the research, developed 
algorithms and the software platform manual. 
8 
 
 
CHAPTER 2: GROUNDWATER VULNERABILITY ASSESSMENT 
METHODS 
2.1 INTRODUCTION 
This chapter discusses various conventional groundwater vulnerability approaches, their merits and 
shortfalls with regard to their application in modelling groundwater vulnerability specific to AMD 
pollution at a regional coalfield scale. A literature review of AMD formation, transport and 
attenuation will be done in view of informing the modelling of AMD-specific groundwater 
vulnerability. An overview of the concept of AI and its current utilisation for groundwater 
vulnerability will also be discussed in this chapter. Finally, a review of the globally accepted regional 
assessment approaches from various fields such as mineral prospectivity mapping, petroleum 
exploration and environmental regulations will be given in a bid to formulate an approach for 
groundwater vulnerability which is specific to AMD pollution at a regional coalfield scale. 
2.2 GENERAL CONCEPT OF GROUNDWATER VULNERABILITY 
Groundwater vulnerability, related to groundwater protection, is intended to evaluate the likelihood 
of pollution reaching the groundwater system after its introduction on the ground surface. General 
aims of understanding groundwater vulnerability at a regional scale range from (NRC, 1993): 
• Policy analysis and development, where the potential for groundwater pollution is assessed 
and policy refined accordingly to protect groundwater resources from possible impacting 
factors which can be brought about by governing policies. 
• Informing land-use decisions, where land-use practice is altered to reflect the potential for 
groundwater pollution. 
• Improving the general education of and awareness among all groundwater users and 
authorities in charge of managing the water resources. 
Similar to other fields of science, groundwater vulnerability is governed by a set of laws from which 
assessment methodologies are formulated. 
  
9 
 
 
2.2.1 Laws of Groundwater Vulnerability 
The three laws of groundwater vulnerability formulated by the NRC (1993) are given as follows: 
First law - The first law of groundwater vulnerability states that all groundwater is to a certain extent 
vulnerable to pollution. Thus, assessments of groundwater vulnerability are meant to give a relative 
likelihood of pollution occurring in the groundwater system after its introduction on the ground 
surface. From the first law, the issue of time-travel of pollution to reach the groundwater should not 
be used as a measure of vulnerability because a longer travel time does not guarantee that the aquifer 
has a low vulnerability. The best approach, in line with the first law, is to consider the extent to which 
processes such dispersion, sorption, dilution, ionic exchanges, and biochemical would contribute to 
the reduction of pollution concentration or to the transformation of pollution to other less 
environmentally damaging products. 
Second law - The second law of groundwater vulnerability states that uncertainty is inherent in all 
vulnerability assessments. Thus, the fundamental problem with an assessment of how pollution will 
behave at the subsurface is limited. Moreover, for any assessment, spatial data are used and these data 
are often derived by interpolation methods which themselves introduce uncertainties. Precise 
knowledge concerning the behaviour of any pollution in the subsurface is limited to the current level 
of understanding of the processes, based on laboratory or field site investigations used to interpolate 
the results to cover the whole assessment area. Thus, owing to the inherent uncertainties, assessment 
should be expressed in probabilistic terms such as “likelihood” or “tendency” so that the inherent 
uncertainty of the assessment is apparent. The most common causes of uncertainty in groundwater 
vulnerability assessments include (NRC, 1993): 
• errors in obtaining input data; 
• errors due to natural spatial and temporal variability; 
• errors in computerisation and storage of data; 
• data processing errors; 
• modelling and conceptual errors; and 
• output and visualisation errors. 
Third law - The third law of groundwater vulnerability states that groundwater vulnerability results 
often obscure obvious differences or make it difficult to discern subtle differences. Thus, while it may 
be easy to identify areas where groundwater is very likely to be polluted it is difficult to delineate 
areas where groundwater is indeed unlikely to be affected by pollution. It is important that 
groundwater classes consider these aspects. 
10 
 
 
In summary, a formulation of groundwater vulnerability assessment methods should adhere to the 
fundamental laws: thus, groundwater is expressed in terms of pollution concentration loads (first law). 
An assessment is done and expressed in probabilistic terms as opposed to providing a precise 
definition of pollution migration mechanisms (second law). Ultimately, the assessment should show 
groundwater vulnerability as high, moderate, low and avoid class names such as “impossible” or 
“difficult” (third law). 
2.3 REVIEW OF GROUNDWATER VULNERABILITY ASSESSMENT 
APPROACHES 
Groundwater vulnerability is a relative dimensionless parameter of the natural attenuation of 
pollutants by the surface and/or subsurface which cannot be measured directly in the field. 
Assessments are often done to understand the natural conditions of the geology, hydrogeology and/or 
can be expanded to include the nature of pollutants and their migration into and interaction with the 
subsurface. This is achieved by geological mapping, pump testing and column leach tests among 
other methods. 
Groundwater vulnerability assessments may be divided into three general categories: 
• overlay and index; 
• process-based simulation model; and 
• statistical approaches. 
2.3.1 Overlay and Index Approach 
This assessment approach is based on combining various geological, hydrogeological and other 
physical attributes deemed to be major factors controlling groundwater pollution. Weights are 
assigned to each attribute by comparing the relative importance of each attribute with groundwater 
vulnerability and its spatial resolution. The attributes are then combined manually or a in GIS 
environment to produce a groundwater vulnerability model (NRC, 1993). This approach is preferred 
because of its relative simplicity. Although data can be obtained easily, the approach includes all the 
important factors of groundwater vulnerability. The most commonly used approaches such as the 
DRASTIC, GOD, SINTACS and AVI will be discussed in this section. 
2.3.1.1 DRASTIC 
The methodology allows for a systematic evaluation of the pollution potential of an area using readily 
available hydrogeological, geological and morphological data which can be obtained and 
meaningfully mapped in minimal time and at minimal cost. The DRASTIC method was developed 
11 
 
 
by the United States Environmental Protection Agency (USEPA) as a proactive tool for the 
assessment of groundwater vulnerability to pollution, and has the following overall goals (Aller et 
al., 1987): 
• function as a management tool; 
• simplicity and ease of use; 
• ability to use available information; and 
• ability to be used by individuals with diverse backgrounds and levels of expertise. 
The method consists of two major elements: the designation of mappable units, termed 
hydrogeological settings and the assignation of relative rankings of hydrogeological parameters. The 
name “DRASTIC” comes from the acronym of the seven parameters which make up the 
methodology: Depth to water table (D), net Recharge (R), Aquifer media (A), Soil media (S), 
Topography (T), Impact of the vadose zone (I) and hydraulic Conductivity (C) of the aquifer. The 
DRASTIC parameters are combined to form one result, termed the “DRASTIC Index” which is 
determined by multiplying each hydrogeological factor weight by its point rating and summing the 
total, as given by Equation 2.1 (Neshat et al., 2014). 

 =  
( ∗ 	) 2.1 
Where 
 is the DRASTIC index value and  is the weigh	ted coefficient (importance weight) for parameter , with an associated rating (class rating) value of . 
Each parameter is divided into classes, each with a rating value weighted based on its relative 
importance in respect to groundwater vulnerability. Each of these hydrogeological factors is given a 
rating from 1 to 10, and the DRASTIC parameters are weighted from 1 to 5 according to their relative 
contributions to the potential pollution. The resulting index is a relative measure of vulnerability to 
pollution where areas with higher index values are more vulnerable than those with lower indices. 
Table 2.1 shows the ranges, ratings and weights for each of the seven parameters making up the 
original DRASTIC methodology as proposed by Aller et al (1987) in the 1980s. These values only 
serve as a guide to which modifications may be made by changing the weights, ratings and by adding 
or removing parameters to suit a particular hydrogeological condition. This would be referred to as 
the modified DRASTIC. The DRASTIC method has two versions; one for intrinsic vulnerability 
(DRASTIC-typical) and one for the specific vulnerability of a particular pollution manifestation 
(DRASTIC-Pollution). The difference between these versions resides in the redefinition of their 
parameter weights and the addition of the pollution scores (Kazakis and Voudouris, 2015). Since the 
12 
 
 
development of the DRASTIC model for groundwater vulnerability assessments by USEPA in the 
late 1980s, this type of indexing method has become popular and generally used worldwide (Al-
Adamat et al., 2003; El-Naqa, 2004; Musekiwa and Majola, 2013; Saida et al., 2017). The advantage 
of the DRASTIC approach includes the usage of many parameters, which ensures that most 
hydrogeological processes are included (Babiker et al., 2005). The method also allows pollution of 
any hydrogeological setting to be systematically evaluated from relatively accessible and available 
data at a reasonable cost (Aller et al., 1987; Metni et al., 2004). 
Table 2.1: Original DRASTIC parameters (Aller et al., 1987) 
 
13 
 
 
Table 2.1 (continued): Original DRASTIC parameters (Aller et al., 1987) 
 
Moreover, the DRASTIC approach is independent of the aquifer type and the weights and ratings can 
be adjusted to suit a particular given hydrogeological setting or climatic condition (Voss and 
Tesoriero, 1997; Al-Hanbali and Kondoh, 2008). However, this method also has several drawbacks 
which have caused many researchers to question the index and overlay methods. 
2.3.1.2 GOD 
The GOD approach is a vulnerability assessment methodology developed in Great Britain, where 
most groundwater resources are in hard rock aquifers, primarily consisting of sandstone and limestone 
covered by unconsolidated overburden or soil layers (Foster, 1998; Harter, 2008). Like DRASTIC, 
GOD is an index-and-overlay method designed for a quick assessment of groundwater vulnerability 
over large regions based on a few important parameters: groundwater occurrence (G), overall 
lithology of the unsaturated zone (O) (overlying aquitard) and depth to the groundwater table (D). 
Scores are assigned to each of the three categories and then multiplied to yield a final score according 
to Equation 2.2 (Draoui et al., 2008). 
 =  ∗  ∗  2.2 
The value of the index varies from 0 to 1 (Table 2.2) and five vulnerability classes, also ranging from 
0 to 1, are differentiated by the method. Because the parameters can only take values from 0 to 1, 
when multiplied together, the overall result is usually a value lower than the score assigned to each 
parameter (Gogu and Dassargues, 2000). 
14 
 
 
Table 2.2: Original GOD parameters (Gogu and Dassargues, 2000) 
 
The advantage of this method is that very few parameters are used and can easily be obtained at a 
very low cost and the method takes into consideration the likelihood of fractures or fracture systems 
developing in the soils, overburden, or overlying geological units of the aquifer. However, owing to 
the use of so few parameters, the model produced is over-simplified in respect of the prevailing 
conditions contributing to groundwater vulnerability. In addition, parameter scores are subjectively 
assigned, making the approach very biased and dependent on the expert’s opinions and level of 
understanding of the hydrogeological processes in the particular area. 
2.3.1.3 SINTACS 
The SINTACS (Civita, 1994, 2010), method was derived from the DRASTIC model and is another 
example of an index and overlay method. SINTACS was developed for vulnerability assessment and 
mapping requirements (medium and large-scale maps) by Italian hydrogeologists, and 
hydrogeological, climatic, and impact settings typical of the Mediterranean countries were chosen. 
The method uses the same seven parameters as DRASTIC, but the rating and weighting procedure is 
more flexible. There are four weight classifications, with the possibility of creating new ones. The 
acronym “SINTACS” represents the seven parameters included in the method: Soggiacenza (depth 
to water, S), Infiltrazione efficace (recharge, I), Non saturo (vadose zone, N), Tipologia della 
copertura (soil cover, T), Acquifero (aquifer, A), Conducibilità idraulica (hydraulic conductivity, C), 
Supeficie topografica (slope, S) (Civita, 2010). 
The assignment of weights and ratings is similar to that of the DRASTIC method. The user encodes 
the input data as functions of the local conditions in each area, and has the possibility of using 
different classifications depending on the circumstances. The SINTACS vulnerability index is 
computed using Equation 2.3: 
15 
 
 
  =  
( ∗ ) 2.3 
Where  is the SINTACS index and   is the rating of each of the seven parameters used and  is the corresponding weight in each class. The final results outline vulnerability classes, where 
higher values represent high groundwater vulnerability and low values represent low groundwater 
vulnerability. 
The SINTACS method is able to distinguish degrees of vulnerability at regional scales where there 
are different lithologies, but it is much less effective at assessing the vulnerability of carbonate 
aquifers, as it does not take into account the peculiarities of karst (Vías et al., 2005). With particular 
reference to an AMD assessment at a regional scale, even though this approach is an intrinsic type, it 
does not factor in regional pathways which would have been useful in understanding how pollutants 
might reach the aquifer system. 
2.3.1.4 AVI 
Stempvoort et al. (1993) developed the aquifer vulnerability index (AVI) method for the assessment 
of groundwater vulnerability by quantifying the vulnerability by hydraulic resistance in respect of the 
vertical flow of water through the protective layers. Hydraulic resistance  is defined by Equation 
2.4: 
 =     2.4 
Where  is the layer thickness and  is the hydraulic conductivity of each protective layer. 
As  has the unit length/time (m/s or m/d), the dimension of  is time. Thus, the resultant can be 
used as a rough estimate of the vertical travel time of water through the unsaturated layers, although 
important parameters controlling travel time such as hydraulic gradient and diffusion are not 
considered (Van Stempvoort et al., 1993). The resultant hydraulic resistance may be reclassified into 
five groundwater vulnerability classes, as shown in Table 2.3. 
16 
 
 
Table 2.3: Vulnerability classes of the AVI method (Fraga et al., 2013) 
 
While the index system is based on an assumption that the vulnerability is a linear superposition of 
artificially specified parameters, studies have shown a nonlinear relationship between vulnerability 
and specific parameters (Neukum and Azzam, 2009). In addition, the ratings and weights are all 
specified artificially by an expert according to subjective judgments which can introduce some bias 
into the overall results (Gogu et al., 2003; Frind et al., 2006; Yu et al., 2010). Finally, otherwise 
continuously varying parameters are discretised (Yu et al., 2010). 
Therefore, the general assumptions for the index and overlay methods include the following (Kazakis 
and Voudouris, 2015): 
• the pollution is introduced at the ground surface; 
• the pollution reaches the groundwater table by precipitation/infiltration; 
• the pollution has the same mobility (velocity) as water; and 
• the approach is best suited to large areas. 
2.3.2 Process-Based Simulation Modelling 
This approach involves solving mathematical equations that govern pollution transport by simulating 
models. Thus, an attempt is made to predict pollution transport in space and time which could include 
a one, two or three dimensional model of the unsaturated and saturated conditions (Brindha and 
Elango, 2015). The modelling is mainly specific to a certain hydrogeological condition and type of 
pollution. Examples of such modelling include: the LEACHM model which was formulated to 
simulate the behaviour of pesticides in the unsaturated zone and include: water flow, runoff, solute 
transport, solute dispersion, sorption, degradation and evapotranspiration, the GLEAMS and the 
PRZM which were designed to assist in management decisions (NRC, 1993). The limitations of the 
process-based simulation include a failure to account for flow and transport processes at spatial scales 
regionally. The approach often requires a large amount of data which are sometimes very difficult or 
very costly to acquire over a large area. 
17 
 
 
2.3.3 Statistical Approaches 
Statistical approaches involve the calculation of the probability distribution of groundwater pollution 
based on the frequency of the pollution, pollution concentrations or pollution probability over an 
aerial extent e.g. logistical regression, principal component analysis, fuzzy logic, analytical 
hierarchical process and kriging (NRC, 1993; Dixon, 2005b; Pathak et al., 2014). While statistical 
methods, similar to other approaches, rely heavy on the quality of data, for statistical methods the 
model is derived from the data. Thus, the higher the data quality the better the model is able to 
represent the actual conditions. In modelling using statistical approaches, some modelling may be 
complex and may require experts in that statistical method to help in the model development. 
Advantages of the statistical approach are that they deal more effectively with differences in scale 
than other approaches and there is a myriad of statistical methods from which to choose to suit a given 
dataset and the current knowledge of the system to be modelled. Thus, the approach is more flexible 
than many others are. 
Considering the benefits of the three approaches (index and overlay, process-based and statistical), a 
hybrid system which takes the benefits from these approaches may be useful. These benefits include 
the simplicity and easily available dataset from the index and overlay approaches, expression 
vulnerability in terms of processes specific to pollution being discussed (from the process-based 
simulation approach) and the availability of statistical methods to combine input maps into one 
vulnerability map (from the statistical approach). 
In this research, the groundwater vulnerability assessments are meant specifically for AMD; hence, 
an understanding of how AMD is formed, transported and attenuated in the subsurface is vital. 
2.4 ACID MINE DRAINAGE FORMATION PROCESSES 
Iron sulphide oxidation produces acidic drainage water, often referred to as AMD. Prediction of AMD 
generation and its properties are key to understanding how dissolved metals from active and past 
mining operations are released into the environment, particularly into the groundwater system 
(Moncur et al., 2009). The prerequisite for AMD is the generation of protons at a faster rate than they 
can be neutralised by any alkaline materials (e.g. carbonates) in the orebody or waste disposal facility, 
access to oxygen and water, and a rate of precipitation higher than evaporation. 
The most common mineral causing AMD is pyrite, but other metal sulphides may also contribute. 
The oxidation of pyrite, preceding iron hydrolysis, occurs in three steps. The first step (Equation 2.5) 
occurs slowly at a pH above 4.3, with high sulphate and low iron concentrations, with little or no 
18 
 
 
acidity (Molson and Aubertin, 2006; Pinetown et al., 2007). The reaction can proceed both abiotically 
and by direct bacterial oxidation: 
 !(") + 7/2'!(() +  )!'(*)  → !, (") + 2 '-!.(/0) + 2),(/0) 2.5 
The second step (Equation 2.6) occurs with a pH range between 2.5 and 4.15 representing high acid 
levels, and where the total iron increases. The Fe3+ /Fe2+ ratio is still low (Pinetown et al., 2007): 
!, (") + ),(/0) + 1/4'!(()  →  3, (") + )!'(*) 2.6 
This stage proceeds predominantly by direct bacterial oxidation determined by the activity of 
microorganisms of the genus Acidithiobacillus (Hedrich and Johnson, 2013). 
The third step (Equation 2.7) occurs at pH values below 2.5, characterised by high sulphate and iron 
levels. The ratio of Fe3+/Fe2+ is high. The reaction is totally determined by bacterial oxidation, that 
enhances the solubility of metal sulphides, catalysed by chemolithoautotrophic acidophile 
microorganisms (e.g. Thiobacillus Ferrooxidans) (Hedrich and Johnson, 2013): 
 ! (") + 15/4'!(() +  1/2)!'(*)  →  3,(") + 2 '-!.(/0) + ),(/0) 2.7 
These three stages are the primary factors, directly involved in the acid production process (Ferguson 
and Erickson, 1988). The intensity of acid generation by these primary factors is determined 
(Salomons, 1995) by environmental (e.g. grain size, pH, temperature, oxygen concentration, metal 
activity) and biological parameters (population density of the bacteria, rate of bacterial growth, supply 
of nutrients). 
AMD is also generated naturally when rocks containing AMD generating material such as pyrite are 
weathered to form an acid solution. The process occurs very slowly, so slowly in fact that the natural 
neutralisation processes readily remove the acidity. However, during mining and mineral extraction, 
the rock mass is extensively fragmented into very small particles, a process which increases the 
surface area and thus increases the rate of acid generation considerably (McCarthy, 2011). 
Geomorphology and the extraction and distribution of AMD generation material are other parameters 
affecting the overall impact of AMD on the surrounding environment. 
It follows that when designing a groundwater vulnerability assessment which is specific to AMD, it 
is important that areas with acid generation material be identified and the availability of water for the 
AMD formation reactions to occur be mapped out. In addition, when AMD is released into the 
environment, owing to the lowering of pH and with high sulphate ad iron concentrations the fate of 
the AMD should be investigated as it passes through the soils, the unsaturated zone below the soils 
and in the aquifer. 
19 
 
 
2.5 SHORTCOMINGS OF GROUNDWATER VULNERABILITY 
ASSESSMENT METHODS 
Based on the understanding of the formation of AMD and considering at the conventional approaches 
discussed in section 2.3, it can be seen that assessment approaches suffer the following pitfalls when 
used for specific groundwater vulnerability assessments at a regional scale: 
• Approaches such as DRASTIC and SINTACS use recharge parameters calculated from soils 
and topography parameters where all these parameters are used to generate the groundwater 
vulnerability model. This means that the output model will increasingly mimic these parameters 
and mask out the effects of other parameters. This is called parameter dependence. Thus, 
parameters need to be redistributed and some removed to reduce the parameter dependence 
problem. 
• The approach mentioned here does not specifically consider fracturing and preferential 
pathways in the modelling, yet when dealing with pollutants such as AMD these would be 
particularly important where some lithological units of a typical coalfield may be fractured. 
• The allocation of rates and weights is subjective and varies from one expert to another. Hence, 
the generated groundwater vulnerability models are often variable and highly debated by many 
experts. 
Thus, the groundwater vulnerability assessment methods need to be able to simulate or take into 
account the effects of fracturing and preferential flows. The review of characteristics and processes 
occurring in the unsaturated zone and the review of models indicated the following knowledge gaps 
need to be addressed in order to produce improved approaches for groundwater vulnerability 
assessment: 
• determination of hydraulic properties in the unsaturated zone (permeability, porosity and water 
retention); 
• inclusion of a proxy which would involve the presence of possible preferential flow, in 
particular short-circuiting (fractures and rocks); 
• inclusion of chemical properties (pollutant – rock reactivity, solubility, volatilisation, sorption 
and degradation) of specific pollutants and groups of pollutants; and 
• inclusion of data mining approaches such AI to reduce the subjective nature of many of the 
groundwater vulnerability assessment approaches. 
20 
 
 
2.6 OVERVIEW OF ARTIFICIAL INTELLIGENCE SYSTEMS 
Artificial Intelligence (AI) is the study and creation of computer systems that can perceive reason and 
act with the primary aim of producing intelligent machines or programs. The intelligence should be 
exhibited by thinking, making decisions, solving problems and, importantly, by learning. AI is an 
interdisciplinary field that requires knowledge of computer science, linguistics, psychology, biology 
and philosophy. 
The question of whether a machine is able to exhibit human-like intelligence has been a subject of 
debate for a number of years. Many have opposed this idea, claiming that highly sophisticated 
behaviour such as love, creative discovery and moral choice will always be beyond the scope of 
machines. Others have accepted that machines can indeed exhibit aspects of human-like intelligence. 
This disagreement remains unresolved. In order to understand AI, it is important to define the concept 
of “intelligence”. Intelligence may be defined in two ways (Negnevitsky, 2005): 
• intelligence is the ability to understand and learn things; and 
• intelligence is the ability to think and understand instead of doing things by instinct or 
automatically. 
The first definition does not include machines, whereas the second definition is more flexible to 
accommodate machines exhibiting intelligence. Thus, for a machine or someone to exhibit 
intelligence, it or he/she should be able to think, learn and/or understand. Thinking may be defined 
as “the activity of using the brain to consider a problem or to create an idea”. Thus, intelligence may 
be defined as “the ability to think, learn and/or understand to solve problems and to make decisions” 
(Negnevitsky, 2005). Humans, animals and machines are capable of this. Fundamentally, AI seeks to 
answer the question as to whether a machine is able to do things which at present are done by humans. 
The field of AI is relatively new, having been formulated in 1943, and having developed steadily until 
the present day. 
Table 2.4 shows the brief history of AI from 1943 to the present day. The table reflects the many 
vagaries that the field has undergone in its ±74 year history. 
 
21 
 
 
Table 2.4: Brief history of Artificial Intelligence 
 
The field of AI has many branches, all of which are connected and share commonalities. The most 
widely used today include: machine learning, expert systems, natural language processing, robotics, 
speech, planning and vision which can be further broken down into various other applications 
22 
 
 
(Logica, 2015). Figure 2.1 shows branches of AI among which, in terms of the present research, only 
the machine learning and expert system are applicable to groundwater vulnerability assessments. 
 
Figure 2.1: Branches of the AI field 
2.7 APPLICATIONS OF ARTIFICIAL INTELLIGENCE IN 
GROUNDWATER VULNERABILITY ASSESSMENTS 
Several authors have applied AI to groundwater vulnerability assessments (Dixon, 2005b; Fijani et 
al., 2013; Nadiri et al., 2015; Baghapour et al., 2016). Fijani et al. (2013) used an integrated approach 
which combines four AI systems (Sugeno fuzzy logic, Mamdani fuzzy logic, Artificial Neural 
Networks (ANN) and neuro-fuzzy) to optimise the DRASTIC method for groundwater vulnerability 
assessments. The four AI models were produced separately and then combined by using the outputs 
as inputs to another ANN to produce one output. The authors termed the approach “Supervised 
Committee Machine Artificial Intelligence” (SCMAI). They applied the approach to estimate 
groundwater vulnerability to nitrate (NO3-N) pollution of Maragheh–Bonab Plain aquifer in Iran. The 
seven parameters of the DRASTIC method were used as training inputs and the NO3-N concentration 
in the borehole as the training output. The results of the Maragheh–Bonab Plain aquifer showed a 
better correlation between the results from the SCMAI with the nitrate concentration testing boreholes 
than from the individual AI models. 
23 
 
 
In another case study, Baghapour et al. (2016) used AI to assess groundwater vulnerability in an 
unconfined aquifer of the Shiraz Plain in Iran. Artificial neural networks were used to estimate the 
groundwater vulnerability of the aquifer using the several parameters of the DRASTIC method as the 
training input and nitrate concentration as the training output. 
Dixon (2005b) used the Fuzzy Expert system to model the groundwater vulnerability of Woodruff 
County of the Mississippi Delta region of Arkansas in the USA. Detailed land-use/pesticide and soil 
structure in conjunction with selected parameters of the DRASTIC method were used. Results 
significantly coincided with field data. 
The neuro-fuzzy technique, which is one of the branches of AI, combines artificial neural networks 
and the fuzzy expert system. This technique was used to assess groundwater vulnerability to nitrate 
pollution in a subbasin of the Illinois River watershed located east of the Arkansas–Oklahoma border 
in the USA (Dixon, 2005a). Four plausible parameters, which are critical in transporting pollutants 
through the soil profile to the groundwater were identified, namely soil hydrological group, depth of 
soil profile, soil structure and land use. 
From the case studies, it was clear that the AI system could be used to produce groundwater 
vulnerability models which correlated well with field measurements when used for nitrate pollution. 
No application of AI in groundwater vulnerability dealing specifically with the AMD pollution of a 
typical coalfield in a geological setting similar to that of the South African Karoo environment could 
be found. However, the success of AI in other geological contexts is promising for its use in the 
development of a groundwater vulnerability assessment specific to AMD at a regional coalfield scale 
in South Africa. 
To validate the groundwater vulnerability models generated from the application of AI, the models 
are compared with a measureable parameter which could be either a pollution tracer or pollution 
already in groundwater (e.g. nitrate is commonly used as a main pollutant indicator of the human 
induced pollution of groundwater) (Gheisari, 2017). The correlation coefficient (	) which is 
sometimes referred to as the Pearson product moment correlation coefficient is used to measure the 
strength and direction of the linear relationship between two variables (Roberts and Roberts, 2000) 
such as the groundwater vulnerability model value and the value of the measured parameter in the 
groundwater vulnerability assessment. 
6The mathematical formula used to calculate the correlation coefficient (	) between two variables (5, ) is given by equation (2.8) (Roberts and Roberts, 2000): 
24 
 
	 = :7(∑ 5!)7−∑(5∑65−)!(∑
 
:75()∑(∑6!6))− ( ∑ 6)! 2.8  
Where 7 is the number of data points and 	 varies between -1 and +1. 
The interpretation of the 	 is given in Table 2.5. 
Table 2.5: Interpretation of the R value (Arikunto, 2002) 
 
W	h!en the correlation coefficient value is squared, the result is called the coefficient of determination ( ) which may be considered an approximate measure of the strength of the linear relationship 
between the variables (Zar, 1999). 
For example, if A and B are related and have a correlation coefficient value (	) of 0.85, then 	! 
would be 0.7225, which means that for the equation relating A and B, B explains 72.5% of the 
variability in A. 
2.8 GLOBALLY ACCEPTED REGIONAL ASSESSMENT 
APPROACHES 
Having understood the fundamentals of groundwater vulnerability and approaches to improve them 
in order to produce a groundwater assessment approach which can be used for AMD assessment, 
various globally accepted regional assessment approaches were examined. These include the well-
known mineral systems approach used for mineral exploration, the petroleum system used for oil and 
gas exploration and the source-pathway-receptor approach which is utilised for environmental 
regulatory purposes. 
25 
 
 
2.8.1 Mineral Systems Approach 
The mineral systems approach was first proposed by Fyfe and Kerrich in 1976 (Wyman et al., 2016) 
and reintroduced to mineral exploration by Wyborn et al. (1994). The mineral systems approach for 
mineral exploration involves an understanding of all geological factors that are required to form and 
preserve a mineral deposit. The approach defines mineral deposits as focal points of much larger earth 
processes operating on a variety of scales to focus mass and energy flux in the formation of mineral 
deposits (Porwal and Kreuzer, 2010; Porwal and Carranza, 2015). The approach emphasises those 
processes that are critical to the formation of a mineral deposit. These processes, among others, 
involve the energy that drives the mineralising fluids (i.e. a source of heat), ligands (fluid) that will 
aid in carrying the metals in solution, fluid migration pathways and trapping sites where the metals 
are precipitated and preserved, ultimately forming mineral deposits (Figure 2.2) (Wyborn et al., 1994; 
Knox‐Robinson and Wyborn, 1997). The approach offers a process-based workflow for mineral 
prospectivity analysis and is neither restricted to a particular geological setting or specific mineral 
deposit type. For these reasons, it is widely used in mineral exploration programmes (Porwal et al., 
2015; Chudasama et al., 2016). Figure 2.2 shows the scale dependence of the approach, where all the 
parameters (energy source, fluid-metal source, migration factor and traps factor) are used for a 
regional systems scale with a radius between 5 and 500 km and only the trap factor is used for camp 
and deposit scales with a radius between 0.5 and 10 km and less than 5 km respectively. 
 
Figure 2.2: Mineral systems approach flow diagram 
26 
 
 
2.8.2 Petroleum Systems 
The “oil system” concept (Dow, 1974) has an ideology parallel to that of the mineral systems 
approach which is based on the identification of oil-source rocks which have led to the development 
of “petroleum systems” (a concept first used by Perrodon in 1980). 
Petroleum systems represent an amalgamating concept incorporating unrelated elements and 
processes in petroleum geology, favouring the accumulation of hydrocarbons in the subsurface 
(Magoon and Beaumont, 1999). The term “petroleum” in petroleum systems describes any compound 
that includes high concentrations of any of the following substances (Magoon and Beaumont, 1999): 
• thermal and biological hydrocarbons and gas found in conventional reservoirs as well as in gas 
hydrates, tight reservoirs, fractured shale and coal; 
• condensates; 
• crude oils; and 
• natural bitumen in reservoirs, generally in siliciclastic and carbonate rocks. 
The term “systems” in petroleum systems describes the interdependent elements and processes that 
form the functional unit that creates hydrocarbon accumulations (Magoon and Beaumont, 1999). The 
critical elements include: a petroleum source rock, reservoir rock, seal rock, and overburden rock and 
the processes of trap formation and the generation-migration-accumulation of petroleum (Magoon 
and Dow, 1994; Railsback, 2017) (Figure 2.3). These essential elements and processes must occur in 
time and space so that organic matter found in the source rock can be expelled from a source rock 
through a migration pathway to a reservoir enclosed by a seal in a trapping configuration where 
petroleum accumulates to form a petroleum deposit (Magoon and Dow, 1994; Magoon and 
Beaumont, 1999). The application of petroleum systems in exploration has led to a significant 
improvement in petroleum discovery (Al-Hajeri et al., 2009). Thus, the petroleum systems approach 
also forms a process based workflow for petroleum exploration and is neither restricted to a particular 
geological setting nor limited to a particular petroleum commodity. No literature on the scale 
dependence of this approach could be found at the time of writing of this thesis. 
27 
 
 
 
Figure 2.3 : Petroleum systems approach flow diagram 
2.8.3 Source-Transport-Attenuation Approach 
In groundwater vulnerability assessments, the approach which is most similar to the mineral systems 
and petroleum systems approaches is the Source-Transport-Attenuation (STA) system described by 
Gurdak and Qi (2012). However, when Gurdak and Qi (2012) applied the STA approach to nitrate 
pollution they were unable to establish a clear correlation with field measurements. Thus, Gurdak et 
al. (2015) modified the approach in order to improve the correlation. The shortfall of the modified 
STA approach in solving the regional assessment of AMD pollution is that it does not clearly define 
the sources of energy driving pollutant migration. Moreover, the approach is also affected by 
parameter dependency. Parameter dependency occurs when one or more parameters used in 
modelling occur more than once or their combined effect affects the resultant modelling output such 
that the output results resemble these parameters only, greatly masking out the effect of other 
parameters (Rahmati et al., 2016). The approach being developed in this research redistributes the 
sources of energy and other parameters to obviate dependence amongst them. 
2.9 SUMMARY 
In the chapter, various approaches used for groundwater vulnerability assessment were described. 
Their strengths and shortcomings with respect to addressing groundwater vulnerability to AMD at a 
regional scale were identified. For the generation of a regional assessment methodology specific to 
AMD, a holistic approach would have to be considered by learning from the successful and globally 
28 
 
 
accepted regional assessment approaches in the field of mineral prospectivity mapping, oil-gas 
exploration and environmental regulatory. 
The findings in this chapter need to be considered in the development of a groundwater vulnerability 
assessment approach which incorporates the nature of the AMD pollution, its production, transport 
and attenuation on the surface and in the subsurface. AI will be used to assist the generation of 
groundwater vulnerability models by incorporating the knowledge and learning patterns from the 
data. 
29 
 
 
CHAPTER 3: DEVELOPMENT OF GIS-BASED GROUNDWATER 
VULNERABILITY ASSESSMENT FOR ACID MINE 
DRAINAGE 
3.1 INTRODUCTION 
A literature review of the various groundwater vulnerability methods was presented in Chapter 2. 
Research gaps and the shortcomings which prevent the methods from fully addressing an assessment 
of groundwater vulnerability to AMD at a regional coalfield scale were identified. 
In this chapter, an approach to assess groundwater vulnerability is developed and discussed. Input 
map layers used for the developed approach are formulated through a series of field and laboratory 
experiments coupled with a consideration of the availability of other relevant datasets. The developed 
approach for a groundwater vulnerability assessment at a regional coalfield scale is parallel and 
analogous to globally accepted regional assessment approaches in the field of mineral prospectivity 
mapping, oil-gas exploration and environmental regulations. Next, the approach will be discussed 
and the input layers formulated. The approach is termed SPT for reference purposes. The acronym is 
derived from elements which make up the assessment (S – Sources, P – Transportation pathways and 
T – Traps). Input map layers for the Witbank, Ermelo and Highveld coalfields will be generated. 
Some parts of this chapter were extracted from Sakala et al. (2018), a publication written as part of 
this research. 
3.2 OVERVIEW OF THE SPT APPROACH 
An approach analogous to the mineral systems, petroleum systems and STA approaches was devised 
for the assessment of groundwater vulnerability to AMD at a coalfield scale following the shortfall 
of the current approaches to groundwater vulnerability assessments. Figure 3.1 shows the process-
based connectivity of the various processes and parameters. According to this approach, the 
topographic gradient is regarded as the energy factor driving the pollution migration processes and 
rainfall as a source of ligands. Pollutant sources are regarded as analogous to metal sources, while the 
transport properties of soil, the vadose zone and the aquifer are correlated with the transport 
component and the subsurface (physical and chemical) trapping properties are correlated with the 
trapping component referred to in the mineral systems approach. 
30 
 
 
 
Figure 3.1: Developed groundwater vulnerability approach flow diagram 
The energy flow through various components of the vulnerability approach is summarised as follows 
(Figure 3.1): 
• The topographic gradient (slope), in particular gravity, acts as the source (S) of energy to drive 
the migration of water from the surface to the groundwater. 
• Rainfall acts as a ligand source (S) of water which carries pollutants to the groundwater and is 
also an input to the formation of AMD formation. 
• Presence and proximity of pollutant sources (S) to the groundwater also play a role in the 
vulnerability of the groundwater system to those particular pollutants. 
• Soil properties, preferential pathways and aquifer media control the vertical and lateral 
movement and transportation pathways (P) of the pollutants or group of pollutants. 
• Pollutants are trapped (T) in the subsurface by physical and chemical processes such as 
sorption, neutralisation, filtration, chemical reactions and dispersion. 
In general, the groundwater vulnerability approach involves the mapping of three broad factors 
(sources, transportation pathway and traps) which are critical to the vulnerability of groundwater in 
respect of pollution. Figure 3.2 illustrates how the selected groundwater vulnerability assessment 
parameters can be related in space. 
31 
 
 
 
Figure 3.2: Schematic illustration of the parameters which make up the proposed 
groundwater vulnerability approach 
The approach is also scale dependent, where all the parameters (energy sources, fluid and pollutant 
sources, transport and traps) are used at catchment/coalfield scale whereas, at a small scale such as a 
mining area, only transport and traps are considered. At a small scale, changes in parameters such as 
the ligands are considered to be insignificant, and are thus not used in the modelling of groundwater 
vulnerability. 
3.3 THE SPT INPUT MAP LAYERS 
This section describes the input parameters which make up the SPT approach and shows how they 
were formulated. The description is given according to the three broad components (sources, 
transportation pathway and traps). 
3.3.1 Sources 
The Oxford English Dictionary (Oxford, 2017) defines “source” as “a place, person, or thing from 
which something originates or can be obtained”. In the SPT groundwater vulnerability approach, 
“sources” thus define the origins of AMD pollution: its formation and the surface morphology which 
controls its initial migration. The developed groundwater vulnerability approach includes three 
components which make up the sources factor whose proxies can be extracted from readily available 
datasets and literature. 
32 
 
 
These parameters are: 
• sources of energy; 
• sources of ligands (water); and 
• sources of AMD pollution. 
3.3.1.1 Sources of energy 
In mineral systems, the hydrothermal fluid drives the movement of ligands and metals to a deposition 
location where a deposit is formed. In the mineral systems approach, the hydrothermal fluid drives 
the movement of ligands and metals to a deposition location where a deposit is formed. In the 
groundwater vulnerability approach, the energy driving the pollution migration process is determined 
by the topographic gradient. The topographic gradient plays an important role as it controls the 
likelihood that pollutants will run off or remain on the surface where they will ultimately infiltrate 
the subsurface (Aller et al., 1987; Goderniaux et al., 2013). 
Several field and laboratory studies have been done in different parts of the world with the overall 
goal of determining the effect of topographic gradient, in particular soil slope angle, on the infiltration 
rate (Nassif and Wilson, 1975; Djorovic, 1980; Sharma et al., 1983; Luk et al., 1993; Fox et al., 
1997). All these studies have observed a decrease in infiltration rates with increasing slope angle 
regardless of soil type. Luk et al. (1993), however, observed that for storms of short duration, the 
infiltration rate increased with increasing slope angle, while for longer storms, the reverse occurred, 
with the infiltration rate decreasing with increasing slope angle. Results from laboratory experiments 
by Fox et al. (1997) show that the relationship between infiltration rate and slope angle is negative 
and non-linear where the infiltration rate decreased with increasing slope angle until 11.5° where the 
infiltration rate remained unchanged at steeper slope angles (Figure 3.3). Slope angles can be 
converted to the topographic slope, a proxy of the topographic gradient, using the relationship by 
Menashe (2004). Thus, a 11.5° slope angle translates to topographic slope of 20.1% as the cut off in 
topographic slope at which point there is no change in infiltration rate (Figure 3.4). With results from 
the same experiment, Fox et al. (1997) also plotted rainwater surface velocity against slope angle and 
established that, as the slope angle increases, so does the overland flow velocity (Figure 3.5). This 
phenomenon can be accounted for by the fact that the lower infiltration rates on steeper slopes 
observed in these experiments were attributable to shorter detention times since flow velocities are 
much greater on steeper slopes than on flat or gentle slopes. 
33 
 
 
 
Figure 3.3: Decreasing mean measured and least-squares mean final infiltration rates with 
increasing slope angle (error bars are ± 1 standard error) 
 
Figure 3.4: Relationship between percentage slope and slope angle 
 
Figure 3.5: Overland flow velocity increases with slope angle (error bars are ± 1 standard 
error) 
34 
 
 
Topographic slope is the measure of steepness or the degree of inclination of a terrain feature relative 
to the horizontal plane and can be easily calculated from contour lines on a topographic elevation 
map. To find the topographic slope of a terrain feature, the horizontal distance (run) and the vertical 
distance (rise) between two points on a line parallel to the terrain feature are determined (Figure 3.6). 
The topographic slope can be obtained using Equation 3.1: 
;<=<(>/=ℎ@ "*<= (%) =  		B"7 ∗ 100 3.1 
  
Figure 3.6: Schematic illustration of the parameters used to calculate topographic slope 
Thus, the smaller the slope values, the flatter the surface and, conversely, the higher the slope values, 
the steeper the terrain. Flat-lying and gentle slope areas are more likely to allow infiltration than 
runoff, making such areas favourable for the infiltration of water and dissolved pollutants. 
Shuttle Radar Topography Mission (SRTM) elevation data with 30 m resolution (USGS, 2016) which 
is freely available to download can be used to calculate the topographic slope in percentage. SRTM 
was an international project spearheaded by the National Geospatial-Intelligence Agency (NGIA), 
National Aeronautics and Space Administration (NASA), the Italian Space Agency (ASI) and the 
German Aerospace Centre (DLR). The project was carried out during an eleven-day mission in 
February 2000 using a specially modified radar system that was flown on-board the space shuttle 
Endeavour. The main objective of the mission was to obtain elevation data on a near-global scale and 
to make the information publically available. 
3.3.1.2 Sources of ligands (water) 
The rate of pyrite oxidation in the mining waste, tailings or subsurface is mainly controlled by the 
availability of oxygen and water at the mineral grain surface (Anawar, 2013). Mining operations 
expose the pyritic material to the atmosphere, making them prone to water and oxygen. Rainfall is 
often a major factor which supplies water for AMD reactions and which acts as a ligand for the 
transportation of products of the AMD reactions as surface runoff or as infiltration. According to 
Chemicool (2017), a ligand is “an ion or molecule that binds to a central metal atom to form a complex 
(alternatively known as a coordination entity)”. In the groundwater vulnerability assessment rainfall 
data can be an event, monthly, annual or average long term and can easily be obtained from a local 
35 
 
 
weather company. Data may take the form of gridded data or rainfall values at several stations where 
the kriging method can be used to interpolate data between stations with gridded rainfall produced. 
3.3.1.3 Mappable sources of AMD pollution 
Sources of AMD pollution range from settling ponds, tailings-cast dumps, opencast pits, waste rock 
dumps, washing plants and loading bays. These sources of AMD pollution can be mapped manually 
by taking global position system (GPS) coordinates of possible sources and taking samples for 
analysis for acid generation potential testing. Another approach for mapping possible AMD sources 
is the use of freely available orbital remote sensing data where the spectral uniqueness of AMD 
generated secondary iron bearing minerals is used to build a decision tree for differentiating these 
from other minerals. 
3.3.1.4 Subsurface sources of pollution 
Subsurface sources of AMD pollution refer to those rock formations under the surface which are 
capable of generating AMD under natural conditions or when exposed to oxygen and water by coal 
mining activities. These include opencast mining, underground workings and coal seams in the 
unsaturated zone, where oxygen and water may be in contact with pyrite rich coal seams and AMD 
can be formed. Information on subsurface sources can be extracted from geology maps where rock 
formations known to contain pyrite are outlined and used as a proxy of the subsurface sources. 
3.3.2 Transportation Pathway 
In the mineral systems approach, hydrothermal fluids transport ligands and metals through 
discontinuous structures (faults, bedding planes, joints, etc.) within the earth’s subsurface and/or at 
the surface. The ligands and metals are concentrated at some preservation location to form mineral 
deposits. In the petroleum system approach, petroleum migrates from organic-rich sediments (source 
rocks) to a reservoir by migrating along fracture pathways. Therefore, the transport mechanism is 
vital to the formation of mineral and petroleum deposits. Similarly, the developed groundwater 
vulnerability approach also incorporates studies of AMD transport in the soil, the vadose zone and 
the aquifer system. 
3.3.2.1 Transportation pathway in soils 
Soils are an independent, dynamic body and occupy the outermost part of the earth’s crust. Soils 
possess distinct morphological, mineralogical, chemical and physical properties inherited because of 
their unique location in space and time and other environmental factors that exist at that location 
(Bear, 1964). Thus, soils are a natural phenomenon controlling the initial transport and attenuation of 
36 
 
 
pollution into the subsurface. Aquifers under soils with physical, chemical and biological properties 
that promote or increase the sorption of pollutants are considered less vulnerable to pollution than 
aquifers without these properties (Mongwe and Fey, 2004). According to Mongwe and Fey (2004), 
an understanding of the various sorption and adsorption mechanisms involved in pollution retention 
is crucial in assessing groundwater vulnerability, as these mechanisms determine the initial rate and 
transport of most pollutants. Soil structure largely governs the size of the soil pores through which 
the pollutants pass. Thus, soils with a high clay content have small pore spaces that reduce infiltration 
and permeability rates (Huddleston, 1994; Mongwe and Fey, 2004) and which, in turn, increase the 
residence time for the chemical removal of pollution by processes such as sorption and adsorption. 
These chemical processes will be dealt with under the attenuation section. 
3.3.2.2 Transport in the vadose zone 
This factor involves those parameters of the vadose zone which are involved in the transport of 
pollution and can be incorporated at a regional scale. In this regard, the parameters chosen include 
the pathways and rock permeability. 
3.3.2.2.1 Preferential pathways 
Possible preferential pathways for AMD and water in the vadose zone may include: contacts of dykes 
and sills with other rocks, faults, fractures and joints (Woodford and Chevallier, 2002). These 
geological features are possible indicators of zones of weakness within the subsurface which may act 
as preferential conduits for the migration of pollutants from the surface to the groundwater. Such 
information can be obtained from published geology and geophysical maps covering the area of 
interest. 
3.3.2.2.2 Rock permeability 
Rock permeability affecting the transport of water and pollutants is measurable. Alternatively, the 
information can be extracted from the geological literature. Rock permeability values of rocks can be 
determined by laboratory tests or fieldwork but this would be very costly. Another option is to 
produce a relative comparison map of rock permeability using published values since groundwater 
vulnerability assessment results present relative comparisons between various areas in terms of the 
likelihood of groundwater pollution. 
3.3.2.3 Transport in the aquifer system 
Aquifer hydraulic conductivity defines the ability of the aquifer material to transmit water (Heath, 
1983; Aller et al., 1987). This also controls the movement of dissolved pollutants. 
37 
 
 
3.3.3 AMD Pollution Traps 
In the mineral systems approach, metalliferous fluids migrate until they reach zones where physical, 
chemical and/or biological processes modify the metalliferous fluid composition, leading to the 
deposition of the metals and the formation of a deposit (Wyborn et al., 1994). Within a groundwater 
vulnerability assessment, subsurface properties seen to inhibit or delay the movement of pollutants 
are regarded as the trapping mechanisms. That is, aquifers overlain by subsurface conditions lacking 
properties that inhibit or delay the movement of pollutants will be vulnerable to pollution. The vadose 
trapping mechanisms considered in this study include physical (soil clay content, depth to water table) 
and chemical (soil clay content, rock-AMD reactivity) traps. 
When AMD is released on the ground surface, the natural attenuation processes of the earth will 
attempt to minimise the effect. The processes of the natural attenuation in soils, the vadose and the 
aquifer play a major role in the attenuation of AMD and are therefore included in the SPT approach. 
3.3.3.1 Chemical traps of acid mine drainage in soils 
The processes promoting pollution attenuation in the subsurface are not quite as obvious and depend 
on many factors, including soil, rock types and the nature of pollution involved. The soils form the 
first part of the unsaturated zone where processes such as sorption, ion exchange, filtration and 
precipitation are some of the processes which contribute to the natural attenuation of major pollution. 
Of these many processes, the ion exchange and precipitation processes will be considered, as they are 
dependent on the nature of the pollutant well as the nature of the unsaturated zone medium. A single 
value describing the potential for the medium to attract cations, the cation exchange capacity (CEC), 
is the most useful parameter in assigning the soil attenuation potential. Thus, CEC can be used as a 
meaningful surrogate for the overall attenuation processes that are likely to occur in the vadose zone. 
Soil CEC is the total of the exchangeable cations that a soil can hold at a specified pH and is known 
to be contributed by clay and organic matter content (Martel et al., 1978; Manrique et al., 1991). 
However, CEC values are not commonly available for the vadose zone or for the soil zone. It is useful, 
therefore, to use the clay mineral content of the vadose zone as a proxy for CEC (Robins, 1998; 
Griffiths et al., 2008). A second part of the attenuation process is controlled by the availability of 
carbon as a catalyst for adsorption and precipitation in the soil medium. Thus, the two key indicators 
used to derive the attenuation potential of the soil and unsaturated zone of the aquifer are clay minerals 
and organic contents. Published soil maps containing this information may be obtained from custodial 
institutes where the soil database of a state or country is held. 
38 
 
 
3.3.3.2 Pollution traps in the vadose zone and aquifer media 
3.3.3.2.1 Depth to water table 
Depth to water table refers to the distance between the ground level and the water table, including 
pore spaces which are partially filled with air and water (Aller et al., 1987; Snyder, 2008). This 
parameter determines the depth of material through which a pollutant or group of pollutants must 
travel before reaching the groundwater system. This distance is important in that it defines the amount 
of time available for various natural attenuation processes which can degrade the pollution. In a 
groundwater vulnerability assessment, depth to water table data can easily be obtained from a 
custodial institute where the groundwater database of a state or country is held. Data can be in the 
form of a gridded contour map or boreholes with water level values where the kriging method may 
be used to interpolate between the boreholes and a gridded depth to water table map produced and 
used for the assessment of groundwater vulnerability. 
3.3.3.2.2 Rock-AMD reactivity 
In order to understand how AMD interacts chemically with various rocks found in a typical coalfield, 
laboratory experiments must be conducted. The overall goal of the experiments is to study how AMD 
interacts with various rocks under typical saturated and unsaturated conditions in the subsurface. 
Using an understanding of the interactions between various rocks and AMD, rocks are then ranked 
according to their abilities to extract AMD pollutants and neutralise capacity. The results from the 
ranking of various rocks in terms of their ability to extract AMD pollutants will be used as one of the 
inputs to the SPT approach. 
3.3.4 SPT Groundwater Vulnerability Modelling 
The SPT approach is a hybrid groundwater vulnerability approach which combines the index and 
overlay, process-based simulation and statistical approaches. Parameters which were extracted from 
popular approaches such as DRASTIC include: depth to water table, aquifer hydraulic conductivity, 
rainfall which replaced recharge, soils and topographic slope. Other parameters which were 
incorporated in the assessment include those which are specific to AMD pollution such as surface 
and subsurface sources of pollution, rock-AMD reactivity, pathways and rock permeability. The input 
map layers can be joined together by an appropriate statistical method: multivariate methods 
(logistical regression, principal component analysis, weight of evidence) or AI. 
39 
 
 
3.4 GENERATION OF SPT INPUT MAP LAYERS FOR THE 
WITBANK, ERMELO AND HIGHVELD COALFIELDS 
The SPT approach involves mapping those properties of the earth’s surface and subsurface which can 
play a role in transport, and trapping of AMD if released onto the surface. To illustrate how the inputs 
for the SPT approach are devised, the Witbank, Ermelo and Highveld coalfields were used as unit of 
study. The massive deterioration of groundwater quality by AMD in these coalfields is a growing 
concern for local authorities; hence such an approach would help in the understanding of AMD at a 
regional coalfield scale. 
3.4.1 Location of the Witbank, Ermelo and Highveld Coalfields 
The Witbank, Highveld and Ermelo coalfields are located between latitude 25o30” to 27o45” South 
and longitude 28o30” and 30o30” East, covering a total area of approximately 27 500 km2 (Figure 
3.7). 
3.4.1.1 Location of the Witbank coalfield 
The Witbank coalfield is situated in the northern part of the main Karoo basin, extending from roughly 
25°30′S to 26°30′S by 28°30′E to 30°00′E, and covering an area of over 568 000 ha. The coalfield 
extends from the town of Springs in the west to Belfast in the east, and from the town of Middelburg 
in the north of the Smithfield ridge (Figure 3.7). The northern boundary of the coalfield is formed by 
pre-Karoo basement rocks, whilst the southern boundary in the central portion of the basin is widely 
considered to be a sub-outcrop against a basement paleo-high known as the Smithfield ridge, a 
broadly east–west trending, crescent shaped ridge of pre-Karoo felsite, granite and diabase of the 
Bushveld Igneous Complex. The Highveld coalfield is located to the west and the Ermelo coalfield 
to the east on the southern side of the Smithfield ridge. The western and eastern edges of the coalfields 
are arbitrarily defined by the sub-outcrop of the coal-bearing sedimentary succession against the pre-
Karoo basement. 
For over a century, this coalfield has been the most important in South Africa, supplying more than 
50% of South Africa's saleable coal. The area produces both metallurgical coal and thermal coal for 
the export and local markets, and hosts many of the major coal-fired power stations in South Africa 
including Kendal, Duvha, Komati and Arnot. The coalfield is named after the city formerly known 
as Witbank, which was renamed to eMalahleni in 2006 (Hancox and Götz, 2014). 
 
40 
 
 
 
Figure 3.7: Location of the study area in relation to provincial and international boundaries 
3.4.1.2 Location of the Highveld coalfield 
The Highveld coalfield is situated in southeastern Gauteng and Mpumalanga Provinces and covers 
an area of approximately 700 000 ha. The coalfield is separated from the Ermelo coalfield by an 
arbitrarily line extending from Hendrina in the northeast, through Davel to the Klip River coalfield 
in the south. The coalfield is bound to the north by Smithfield ridge which separates it from the 
Witbank coalfield. On the western side, the coalfield is bordered by outcrops of granite and rocks of 
the Witwatersrand Supergroup. The southern boundary is located south of Standerton along the Klip 
River to its confluence with the Vaal River, and from there along the Vaal River. Economically, the 
coal resources within the Highveld coalfield are important to the long-term life of Sasol's Synthetic 
Fuels and Sasol Chemical Industries, which require some 50 million tonnes a year (Hancox and Götz, 
2014). 
3.4.1.3 Location of the Ermelo coalfield 
The Ermelo coalfield is a fair producer of coal, but over the past two decades production has declined 
because of the thinner coal seams (Snyman, 1998; Jeffrey, 2005). However, since 2004, this coalfield 
has seen an increase in exploration and mining activities owing to the higher quality of its coal as 
compared to the Witbank and Highveld coalfields, and its proximity to the Richards Bay Coal 
Terminal from where coal is exported overseas. The Ermelo coalfield is located in the districts of 
41 
 
 
Carolina, Dirkiesdorp, Hendrina, Breyten, Davel, Ermelo and Morgenzon in the southeastern part of 
Mpumalanga Province. The coalfield extends approximately 75 km east–west, and 150 km north–
south, covering an area of about 1 125 000 ha (Hancox and Götz, 2014). The northern and eastern 
boundaries of the Ermelo coalfield are defined by the sub-outcrop of the coal-bearing strata against 
the pre-Karoo basement. In the west, the Ermelo coalfield shares a boundary with the Witbank and 
Highveld coalfields and, to the south, with the Klip River and Utrecht coalfields of KwaZulu-Natal 
(Greenshields, 1986). 
3.4.2 Physiography 
The area receives average long-term rainfall of between 600 to 1 100 mm (ARC-ISCW, 2014). The 
winters are typically dry and cold with occasional frost, while the summers, between October and 
March, are hot (Barnard, 2000). The altitude ranges from 1 225 m to 2 237 m metres above sea level 
(m.a.s.l) with the Olifants River and its tributaries being the main drainage system. 
With reference to climatic data collected between 1982 and 2012 recorded at the eMalahleni, Ermelo, 
Sanderton and Volkrust stations, the study area receives monthly rainfall of between 2 mm in June 
and 150 mm in December (Climate-data.org, 2017). The monthly distribution of average daily 
maximum temperatures shows that the average midday temperatures for the study area range from 
2 °C in July to 26 °C in January with July as the coldest month (SAWS, 2016). 
According to the Köppen climate classification, the study area falls in the Cwb class. Areas in the 
Cwb class are characterised by a subtropical highland climate with dry winters. Temperatures in the 
coldest month average above 0 °C, and all months have average temperatures below 22 °C. In at least 
four months, temperatures average above 10 °C, with at least ten times more rain in the wettest month 
of summer than in the driest month of winter (Geiger, 1954). Figure 3.8 shows the typical temperature 
and rainfall distribution throughout the year. 
Understanding the climatic conditions of the study area is particularly important in view of the fact 
that AMD generation is controlled by the climate and one of the key reactants (water) directly depends 
on climatic conditions. In general, South Africa has a very pronounced east–west climatic gradient 
with rainfall decreasing from over 1 000 mm/a in the east to less than 100 mm/a in the west. Potential 
evapotranspiration increases from about 1 500 mm/a in the east to 3 000 mm/a in the west, causing 
most of the country (including the study area) to experience a negative water balance (i.e. 
evapotranspiration <rainfall) (McCarthy, 2011). When rain falls on exposed pyrite/sulphide minerals 
in a strongly evaporative environment, it is less likely that the acidity or toxicity of produced products 
will be diluted. Thus, any rainfall event affecting exposed pyrite/sulphide minerals would contribute 
significantly to AMD reactions and the concomitant transport of the products. 
42 
 
 
 
 
Figure 3.8: Climatic data for the Ermelo station showing temperature and rainfall 
distribution throughout the year 
3.4.3 Geological and Hydrogeological Setting 
An understanding of the geological and hydrogeological setting is particularly important as the natural 
attenuation properties of the subsurface are derived from this information. 
3.4.3.1 Regional geology 
The Witbank, Ermelo and Highveld coalfield are found in rocks of the main Karoo basin (MKB). 
This basin outcrops over more than half of South Africa (Figure 3.9) and forms part of a major series 
of Gondwana basins that developed through subduction, compression, collision, and terrane accretion 
along the southern margin of Gondwana. This series includes the Paraná basin in South America, the 
Beacon basin in Antarctica and the Bowen basin in Australia (Hancox and Götz, 2014). The 
sedimentary filling of these basins is particularly important from a geological and palaeontological 
perspective in that they contain an almost unbroken record of 120 million years the history of the 
earth, at a period when the Pangaean supercontinent had reached its maximum extent, and during 
which major evolutionary changes were taking place (Hancox and Götz, 2014). The economic 
significance in terms of energy resources of these sedimentation events is that they brought about 
important energy resources (coal, coal bed methane, shale gas and uranium) which are vital to the 
economic development of the country. 
The sedimentary part of the main Karoo basin Supergroup is subdivided into four main 
lithostratigraphic units: the Dwyka, Ecca, Beaufort and Stormberg Groups (Molteno, Elliot and 
Clarens Formations) (SACS, 1980; Johnson et al., 1996). The lithostratigraphic units which host coal 
43 
 
 
deposits in South Africa include the Ecca Group (Vryheid Formation), Beaufort Group (Emakwezeni 
Formation) and the Molteno Formation.  
 
Figure 3.9: Extent of the Karoo basin in South Africa, with coalfields. The blue line indicates 
the location of the cross-section AB shown in Figure 3.10 
During the Permian–Carboniferous, a period of glacial sedimentation marked the start of various 
sedimentation events which gave rise to the Karoo Supergroup (Lindeque et al., 2011). In the glacial 
sedimentation period, the diamictites and associated fluvio-glacial sediments (Dwyka Group) were 
deposited. A shallow sea remained after the glaciation event which led to the deposition of the black 
clays and muds which form the lower Ecca Group. The prevailing cold climatic conditions and 
submerged environments favoured this deposition event and deltas progressed towards the sea which 
later combined to form broad alluvial plains that make up the upper Ecca Group. As the glacial ice 
sheet retreated northwards, the glacial valleys were filled by fluvioglacial sediments such that shallow 
postglacial lakes were formed, which were transformed into swamps resulting in the formation of the 
lower coal seams directly overlying the sediments of the Dwyka Group in the Witbank, Highveld, 
Free State and Vereeniging–Sasolburg coalfields. After the deposition of the Ecca Group, the 
prevailing semi-arid environment possibly led to the deposition of the Beaufort Group in the alluvial 
plains of the basin. This occurred towards the end of the Triassic. 
Economic deposits of coal are restricted to the northeastern section of the basin in the Ecca Group. 
The lower coal seams found in the Ecca Group reflect the pre-Karoo valleys and mountains and the 
upper coal seams mark the basinward extent of the delta as it progresses towards the basin margin. 
44 
 
 
The main Karoo basin is largely underlain by a stable floor, comprising the Kaapvaal Craton in the 
north and the Namaqua-Natal Metamorphic Belt in the south, and is bounded along its southern 
margin by a fold-thrust belt known as the Cape Fold Belt. The basin is thick in the south and thins 
towards the north as shown on the regional S–N geological cross-section (Figure 3.10). 
 
Figure 3.10: Schematic north–south section across the main Karoo basin 
There are nineteen coalfields in South Africa (Figure 3.9), with current mining activities largely 
taking place in the Witbank, Ermelo and Highveld coalfields of Mpumalanga Province (Banks et al., 
2011). 
3.4.3.2 Local geological setting 
The local geological information used in this study was drawn from 1:250 000-scale geological maps 
(Pretoria 2528 and East Rand 2628) published by the Council for Geoscience (Figure 3.11). The study 
area comprises eight major lithological domains, namely: 
• Basement Complex;  
• Witwatersrand Supergroup;  
• Transvaal Supergroup; 
• Bushveld Complex;  
• Dwarsfontein Complex; 
• Waterberg Group; 
• Karoo Supergroup; and  
• Tertiary–Quaternary alluvial deposits. 
45 
 
 
 
Figure 3.11: Local geology of the study area mapped at a 1:250 000 scale showing borehole 
locations 
3.4.3.2.1 The Basement Complex  
In the study area, the oldest rocks are leucocratic biotite granite of the Swazian Era with a small 
exposure in the south-eastern part of the study area. Figure 3.12 shows the rock exposure of the granite 
displaying signs of exfoliation. 
46 
 
 
 
Figure 3.12: Rock exposure of the granites found in the study area 
3.4.3.2.2 The Witwatersrand Supergroup 
The Hospital Hill Formation is the only member of the Witwatersrand Supergroup found in the study 
area, with its outcrops being exposed near Delmas. The outcrops consist primarily of shallow-marine 
orthoquartzites, siltstone, outer-shelf shales and iron formation (McCarthy, 2006). 
3.4.3.2.3 The Transvaal Supergroup 
The sedimentary and volcanic rocks of the Transvaal Supergroup are found in the northern part of the 
study area and lie north of the Karoo Supergroup outcrops. According to SACS (1980), the rocks of 
the Transvaal Supergroup represent a tectono-sedimentary phase of clastic, volcanic and chemical 
sedimentation within a large sedimentary basin resting unconformably on Swazian basement rock. 
The Transvaal Supergroup in the study area is represented by the Chuniespoort, Pretoria and Rooiberg 
Groups and the Loskop Formation. The Malmani Subgroup of the Chuniespoort Group comprises 
chert and dolomite with only minor clastic sediments (Button, 1973). In the study area, dolomites of 
the Malmani Subgroup are found around Delmas and exposed rocks are greyish in colour with an 
elephant skin-like texture (Figure 3.13). The Pretoria Group is the uppermost group of the Transvaal 
Supergroup and is unconformably overlain by the Rooiberg Group. The Pretoria Group mainly 
comprises mudrock alternating with quartzitic sandstone, subordinate conglomerate, diamictite, 
interbedded basaltic-andesite lavas and carbonate rocks (Eriksson et al., 2006). 
47 
 
 
 
Figure 3.13: Malmani Subgroup dolomite rock exposed in the study area displaying an 
elephant skin texture 
Exposed mudrocks of the Pretoria Group within the study area clearly show bedding planes and 
fractures (Figure 3.14). The Rooiberg Group consists of rhyolite and felsite forming the roof of the 
intrusive Bushveld Complex and represents the first igneous activity associated with the complex 
(Buchanan and Reimold, 1998). In the northern extremity of the study area, the Rooiberg Group 
grades conformably into the Loskop Formation, with the latter consisting of 1 100 m of red shale 
intercalated with conglomerate in the lower part and mainly impure quartzite in the upper part 
(Clubley-Armstrong, 1977; Martini, 1999). 
 
Figure 3.14: Pretoria Group mudrock outcrop showing heavy fracturing and bedding planes 
3.4.3.2.4  Bushveld Igneous Complex 
The Bushveld Igneous Complex occurs in the northeastern part of the study area. The complex is 
mainly represented in the mapped area by the Rustenburg Suite, a succession of mafic and ultramafic 
layered rocks including gabbros, norites, diorites, anorthosites and gabbronorites (Barnard, 2000). 
The Lebowa Suite, representing a younger felsic phase occurs as a single granite pluton is named the 
Nebo granite and is found in the north-eastern part of the study area. 
48 
 
 
3.4.3.2.5 Waterberg Group 
The Waterberg Group is a sedimentary suite of rocks consisting of medium- to coarse-grained 
sandstone with interbedded conglomerate and shale (Barnard, 2000). In the study area, the Waterberg 
Group is represented by the Wilge River Formation. 
3.4.3.2.6 Karoo Supergroup 
The Karoo Supergroup was deposited in a vast intracratonic basin reaching its maximum depth in the 
south and in a few satellite basins to the north (Du Toit and Sonnekus, 2014). The Karoo Supergroup 
consists of a variety of sediments that reflect the environmental changes during the migration of the 
Gondwana continent over a period of 200 million years from polar to lower latitudes (Du Toit and 
Sonnekus, 2014). These sediments, covering over 80% of the study area, represent the northern tip of 
the main Karoo basin in South Africa (Figure 3.10). Three main groups are found in this part of the 
Karoo basin. These are the Ecca and Dwyka Groups and the dolerite intrusive rocks. The Dwyka 
Group sediments consist mainly of diamictite (tillite) which are generally massive with little jointing, 
but may be stratified in some places (Woodford and Chevallier, 2002). The Ecca Group (Vryheid 
Formation) consists of undifferentiated grit, sandstone (Figure 3.15), shale and coal seams with 
interlayered siltstone and mudstone comprising up to five mineable coal seams (Hancox and Götz, 
2014). 
 
Figure 3.15: Weathered sandstone outcrop in the Witbank coalfield 
Several dolerite intrusions are found within the study area. The intrusions represent the roots of a 
volcanic system. The Karoo dolerite system consists of an interconnected network of dykes and sills 
and it is therefore nearly impossible to single out any particular intrusive or tectonic system. It is 
likely that a very large number of features were intruded simultaneously by magma and that the 
dolerite intrusive network acted as a shallow stockwork-like reservoir. The emplacement of dykes in 
49 
 
 
the study area appear to be lithologically controlled, as seen by a sharp decrease in intrusion density 
at the boundary between the Ecca and Beaufort Groups. The bulk of the dykes are stratabound and 
concentrated in the Beaufort Group in the southern part of the study area. In general, dolerite dykes 
develop by rapid hydraulic fracturing via the propagation of a fluid-filled open fissure, resulting in a 
transgressive contact with the country rock. They develop vertically upwards or laterally along strike 
over very long distances. 
3.4.3.2.7 Quaternary deposits 
According to Woodford and Chevallier (2002), Quaternary deposits are a common characteristic 
along the major rivers in the Karoo basin. Deposits on the beds of braided streams consist mainly of 
coarse sediments, conglomerates and patches of finer material on their banks while meandering 
streams deposit mainly fine-grained sand, mudstone and siltstone (Gomo and Van Tonder, 2013). 
The geology of the study area is summarised in Table 3.1 with the spatial arrangement of the 
geological features shown in Figure 3.11. 
Table 3.1: Summary of the geology of the Witbank, Ermelo and Highveld coalfields 
 
50 
 
 
3.4.3.3 Hydrogeological setting 
The hydrogeological setting of the Witbank, Ermelo and Highveld coalfield also contributes to 
defining pollution migration mechanisms. Thus, the contribution of the hydrogeological setting 
(aquifer types and hydrochemistry) of these coalfields to groundwater vulnerability will be discussed. 
3.4.3.3.1 Aquifer types 
The study area falls within the Johannesburg 2526 and the Nelspruit 2530 1:500 000-scale 
hydrogeology maps. Therefore, the hydrogeology background for the study is based on the 
explanations of these two hydrogeology maps (Barnard, 2000; Du Toit and Sonnekus, 2014). The 
aquifers for the study area are divided into four classes: 
• Intergranular – Mainly alluvial deposits of limited lateral extent and thickness along many river 
terraces; 
• Fractured – Represented by the Witwatersrand Supergroup, Pretoria Group quartzites, the 
Waterberg and Dwyka Groups; 
• Fractured and intergranular – Represented by the Rooiberg Group, the Loskop Formation, the 
Bushveld Complex, the Ecca Group, the Karoo dolerite dykes and sills, the Pretoria Group; and 
• Karst – Limestone and dolomites of the Chuniespoort Group. 
In the Witbank, Ermelo and Highveld coalfields, the most dominant aquifer system is the fractured 
and intergranular type found in the weathered sediments at the interface between the soil and the 
bedrock and occurs at depths of between 5 to 12 m below the surface (Pinetown and Boer, 2006). The 
shallow depth of this aquifer system makes it highly susceptible to pollutants as a result of the reduced 
distance that these have to cover in order to reach the aquifer system. 
The Ecca Group rocks of the Karoo aquifers occupy extensive parts of the study area and comprise 
sandstones, shales and coal layers with the sandstones and coal usually forming reasonable aquifers, 
while the shale serves as an aquitard (Burger, 2012). Layered aquifers are commonly perched on the 
relatively impermeable shale. The groundwater is generally associated with fractures and joints which 
develop along the bedding planes, lithology contact zones and in proximity to structural geological 
features such as shear zones, faults and dykes (Barnard, 2000). The quality of the groundwater in the 
Ecca Group rocks is generally considered to be excellent in areas where no mining operations have 
been carried out, but in the vicinity of mining operations and downstream of these operations the 
quality deteriorates, displaying the characteristic AMD footprint of elevated concentrations of 
sulphates and heavy metals and a low pH. 
51 
 
 
The Dwyka Group which comprises consolidated products of glaciation (with high amounts of clay) 
is normally considered to be an aquiclude owing to low permeability values associated with the rocks 
of this group. However, where the Dwyka Group is highly weathered, permeability increases and 
when a borehole is drilled in such areas the rocks may supply a reasonable yield for a household 
(Barnard, 2000). The chemistry of the groundwater in the Dwyka Group is generally considered 
suitable for domestic and irrigation uses. Background sulphate values range between 1 and 93 mg/L 
based on 46 samples extracted from boreholes drilled in the Dwyka Group in South Africa, but not 
necessarily within the study area. These values may vary owing to other factors such as variability in 
the mineral composition of the Dwyka Group rocks depending on their depositional location.  
Abundant Karoo dolerite intrusions outcropping mostly in the south (Figure 3.16) comprise sills, 
which vary from being concordant to transgressive and feeder dykes. In terms of hydrogeology, the 
dykes are vertical to sub-vertical discontinuities that in general represent thin, linear zones of 
relatively higher permeability which act as conduits for groundwater flow within the aquifer. They 
may also act as semi to impermeable barriers to the movement of groundwater. The high permeability 
of the dyke contact zone is a result of shrinkage joints that developed during cooling of the intrusion. 
Intrusion of dolerite results in localised metamorphism of the country rock which increases the 
porosity within the localised zone. Thus, in Karoo sediments found in the study area, high yielding 
aquifers are localised in proximity to dykes and sills. Although these structures serve as aquitards 
they tend to compartmentalise the groundwater regime and their contact zones with the pre-existing 
geological formations also serving as groundwater conduits (Burger, 2012). These zones also may 
form preferential pathways for pollutants to reach the groundwater system. The special alteration of 
the hydrogeology brought about by dykes and sills needs to be considered when formulating 
groundwater vulnerability approaches. The preferential pathway parameter will accommodate the 
special condition played by the dykes and sills. 
Karst aquifers are also found in the northwestern part of the study area at the town of Delmas. These 
aquifers belong to the dolomites of the Malmani Subgroup of the Chuniespoort Group and are 
considered to be very important aquifer systems in South Africa owing to their high yield which is in 
excess of 5 L/s. This aquifer system is formed when weakly acidic rainwater dissolves carbonate 
minerals found in the dolomite along planes of weakness such as faults, fractures and joints. 
The process of dolomite dissolution may be summarised by Equation 3.2 given by Barnard (2000): 
/'3. 2E('3 + 5)!'3  → 3/()'3)! + 2E(()'3)! 3.2 
G<*<HI + @/>J<7@ /@ → @/*@BH − J@/>J<7/I + H/(7"BH − J@/>J<7/I  
 
52 
 
 
 
Figure 3.16: Hydrogeological setting of the study area 
The resultant soluble bicarbonate is easily washed away in solution, leaving behind openings which 
can be filled with water, making up the aquifer system. The openings may be interconnected to form 
large groundwater storage reserves. 
In terms of karst specific groundwater vulnerability mapping, no standardised approach has been 
developed specific to South African karst terrains. The only comprehensive available study focussing 
on groundwater vulnerability in karst terrains is the COST action 620 (Zwahlen, 2003). Groundwater 
is stored in karstic voids that develop around the conduits and are connected by high water head loss 
zones (Leyland et al., 2008). The large magnitude strong permeability contrast between the matrix 
and conduits renders the storage in the matrix negligible. Recharge of karst aquifers can occur in 
53 
 
 
various ways, as stated by Gunn (1986). Figure 3.17 illustrates the various ways in which karst 
aquifers can be recharged: 
• directly from an infiltration zone from closed points breakings such as sinkholes and shallow 
holes; 
• diffuse through epikarst; 
• stream-sink; or 
• through permeable cap rocks. 
 
Figure 3.17: Conceptual model of a karst aquifer 
Karst aquifers are often characterised by a dual or triple porosity comprising solution voids, fractures 
and the rock matrix (Leyland et al., 2008). The fractures and the rock matrix provide the groundwater 
storage and the conduits act as transportation pathways. Thus, transport of dissolved pollutants in 
54 
 
 
karst aquifers is a fast advective transport similar to fractured aquifers, where pollutants migrate 
mostly along the voids as compared to through the matrix. Thus, karst aquifers have unique properties 
which should be taken into account during a vulnerability assessment. Karst aquifer vulnerability 
assessment methods are usually either methods especially dedicated to karst or methods that, although 
applicable to all aquifer types, contain special methods to be used when being applied to karst areas. 
Since karst aquifers are only localised at a small area within the study area, the special properties of 
karst will be generalised in the development of a groundwater vulnerability approach for a coalfield. 
Owing to the shallowness of the groundwater systems in the study areas, there is an urgent need for 
a groundwater vulnerability assessment to be conducted to highlight sensitive areas to study the ease 
with which pollutants can migrate and enter the groundwater system. As has been mentioned, the 
study area represents over 100 years of coal mining activities and there are new areas that are still to 
be mined. Therefore, it is important that areas identified for possible mining first be subjected to a 
groundwater vulnerability assessment. 
3.4.3.3.2 Hydrochemistry 
Hydrochemistry data used in this research were collected from several boreholes during the dry 
season of July 2013 using conventional best practice groundwater sampling guidelines, as described 
by Weaver et al. (2007). The uses of boreholes in the study area range from domestic, monitoring, 
industrial and irrigation, where groundwater is extracted from shallow phreatic aquifers. 
Sampling was accompanied by recordings of physical parameters (pH, electrical conductivity and 
total dissolved solids) using Aquaread GPS multi-parameter aquameters. Fifty-two (52) groundwater 
samples were collected within the study area (Figure 3.18) in sets of three, filtered, preserved and 
transported in a temperature-controlled environment to the Council for Geoscience laboratory in 
Pretoria where they were analysed for cations, anions and alkalinity using inductively coupled plasma 
mass spectrometry (ICP-MS), ion chromatography (IC) and spectrophotometry respectively. 
Sample duplicates and blanks (deionised water) were used to evaluate analytical consistency and 
errors. The results showed relative percentage differences lower than 10% for duplicate samples and 
below detection limit for the blank samples. Data quality was assessed using the anion-cation balance 
electroneutrality method (Hounslow, 1995), where all the water samples were below the acceptable 
±5% error. 
 
55 
 
 
 
Figure 3.18: Locations of groundwater samples used in this study 
The variability in groundwater chemistry may be attributed to the natural chemical evolution of the 
groundwater chemistry resulting from water-rock interaction and anthropogenic influences 
(Hounslow, 1995). Groundwater samples were classified on the basis of the composition of the major 
ions composition and results presented in a Piper diagram (Figure 3.19). The diagram shows the 
presence of at least two main water types: Ca-HCO3 and the Ca-Mg-SO4 named groups I and II 
respectively with few samples belonging to the Na-HCO3 types. 
56 
 
 
 
Figure 3.19: Piper diagram showing the major water classifications in relation to the TDS 
concentration 
Group I samples reveal a chemical composition resulting from weathering processes affecting the 
regional rocks. According to Bartolino and Cole (2002), the Ca-HCO3 type shows early stages of 
water-rock interaction which often takes place at a shallow depth where the rock mineralogy does not 
significantly influence the composition of groundwater. 
On the other hand, Group II water samples are characterised by high TDS values greater than 
600 mg/L and high SO 2-4  greater than 200 mg/L. The TDS-sulphate scatter plot (Figure 3.20) shows 
a very high coefficient of determination value of 0.924 which means that the hydrogeochemical 
reactions enriching sulphates into the groundwater are contribute about 92% to TDS values. 
57 
 
 
 
Figure 3.20: Scatter plot of TDS against sulphate concentration 
Considering the location of the study area, the most likely processes which add sulphate into the 
groundwater are AMD reactions. The orebodies, waste rock and tailings dumps in the mining areas 
are rich in sulphate minerals which react with water and oxygen to form SO 2-4 , Fe compounds and 
H+ ions (Wild, 1996). The AMD generation reaction produces H+ ions which are responsible for the 
low pH values of samples of group II. As the AMD generation reaction produces more SO 2-4  ions 
into the system, this changes the anion chemistry from juvenile HCO 2-3  dominance to SO 2-4  
dominance. The black arrow in Figure 3.19 shows the possible evolution route of the groundwater 
system from HCO 2-3  to the SO 2-4  water type. The majority of the sampled boreholes fall within the 
blue inverted triangle of the Piper diagram which does not show the most dominant cation, possibly 
due to groundwater mixing. The red points in Figure 3.19 are characterised by very high sulphate, 
high TDS and very low bicarbonate, indicating an origin from mine water where the bicarbonates 
have been depleted by acidity. 
3.4.4 Mining Activities and their Contribution to AMD Pollution 
3.4.4.1 Coal mining history of the Witbank, Ermelo and Highveld coalfields 
In South Africa, the first recorded discovery of coal was in 1699 at Franschhoek in the Western Cape, 
but there are claims supported by scant evidence that the indigenous inhabitants of South Africa may 
have exploited some of the easily accessible coal reserves before the arrival of European settlers. The 
opening of the T and DB Mine located in what is now known as the Witbank coalfield in the 1890s 
caused the coalfield to become the principal energy source of power generation for the country’s 
industries, mines and rail systems. Since the 1890s, the coalfield has been mined to fuel power 
stations. 
58 
 
 
3.4.4.2 Coal geology 
In general, the coal-bearing horizons in the Karoo coalfields are the result of peat accumulations at a 
broad subsidence and in-filled geosynclinal basin at discrete intervals during the evolution of the 
Karoo sequence leading to many coal seams found in the coalfields (Hancox and Götz, 2014). 
3.4.4.2.1 Witbank coalfield  
The Witbank coalfield is a multiple seam deposit type with five major seam horizons having 
developed there. The primarily economic coal seams have been the no. 2 and 4 seams, the 4 lower 
seam and, in some places, the no. 5 seam. Structurally, the coal horizons are undeformed with each 
layer displaying a very slight dip to the southeast of less than a degree and minor discrete faulting 
events that have a southwest to northeast trend of graben features and other minor faulting events. 
The most distinctive post-depositional feature is the intrusion of dolerites related to the Lesotho 
basalts that has resulted in a variety of sills and dykes of various ages. 
3.4.4.2.2 Highveld coalfield 
The coalfield is host to up to five coal seams contained within the middle Ecca Group sediments of 
the Karoo Supergroup. The five identified coal seams contained in the Vryheid Formation are named, 
from the base up, as follows: no. 1, 2, 3, 4, and 5. The coalfield is characterised by the fact that in the 
northern regions, all the coal seams, with the exception of the no. 3 seam, attain mineable thicknesses 
with economic potential while, in the southern regions, only the no. 4 seam and, in very localised 
areas, the no. 2 seam, attain mineable dimensions of economic importance. These intrusive dolerite 
sills and dykes are related to the Drakensberg Formation flood basalts and adversely affect the coal 
seams in the vicinity of the intrusions in terms of coal quality by devolatilising and burning the coal. 
The bulk of the coal produced is consumed in power stations and syn-fuel production (Exxaro, 2006). 
3.4.4.2.3 Ermelo coalfield 
There are five major coal seams which are developed in the Ermelo coalfield, named from the base 
up: E, D, C, B and A seams. The seams are relatively unaffected by folding although faulting and 
associated dolerite (igneous) intrusions are common throughout the coalfield. Dolerite intrusions take 
the form of vertical to near-vertical dykes, often intruding existing faults and sills, which are parallel 
to the bedding planes. Sills are also often transgressive, resulting in the relative displacement of the 
strata. The number of sills increases to the south and up to eight major sills has been identified. An 
additional effect of the dolerite intrusions is the burning or devolatilisation of coal in close proximity 
to the dolerites (Exxaro, 2006). 
59 
 
 
3.4.4.3 Coal mining activities and their impacts to the environment 
Within the Witbank, Ermelo and Highveld coalfields, coal mining started over a century ago with 
both opencast and underground mining, each having its own impact on the environment and health 
in general. Some mining operations have since been abandoned, and some established at new 
locations. The environmental effects caused by coal mining in the Witbank, Ermelo and Highveld 
coalfields include collapsed ground over areas where underground mining was done, with coal fires 
and drainage (acid, neutral or alkaline) emanating from the mining activities. Ultimately, the drainage 
enters the groundwater and surface local river systems such as the Olifants River, if not controlled. 
Figure 3.21 shows surface flow of AMD from an operational mine being discarded to a local stream 
connected to a major river. 
 
Figure 3.21: AMD surface flow from a coal mining operation south of Carolina in the Ermelo 
coalfield. The brownish-orange colour is attributed to iron hydroxyl precipitation 
The AMD which enters the surface river network ends up in major reservoirs such as the Middelburg 
and Witbank dams. Although the AMD is neutralised, the concentration of salts and sulphates remains 
high in solution. For example, the sulphate concentration of the Witbank dam is now over 200 mg/L, 
which exceeds the maximum recommended domestic use such that ESKOM, the leading electricity 
generating company located within the study area imports water from the eastern escarpment for use 
in its power stations (McCarthy, 2011). This prompts the need for a groundwater vulnerability 
assessment to be done with a specific focus on the AMD pollution of the coalfields. 
This research, based on a holistic approach, mainly focusses on differentiating between sensitive and 
non-sensitive areas in a typical coalfield affected by AMD pollution as an environmental issue. The 
resultant models generated would go a long way in advising policy and decision makers on how to 
handle different geological, hydrogeological settings and appropriate mitigation measures suggested 
which would minimise groundwater pollution from coal mining activities. 
60 
 
 
3.4.5 SPT Inputs for the Witbank, Ermelo and Highveld Coalfields 
3.4.5.1 Sources of energy (topographic slope) 
In the study area, the elevation data at spatial resolution of a 30 x 30 m grid cell size was extracted 
from the USGS (2017). The elevation ranges between 1 225 and 2 237 m.a.s.l, with the highest areas 
located in the Upper Vaal catchment area within the Ermelo coalfield (Figure 3.22). The Usutu-
Mhlathuze catchment is at the lowest elevation compared to other catchments. Most of the Witbank 
coalfield lies in the Olifants catchment, with the Olifants River being the main drainage system. 
Several catchments that drain the Ermelo coalfield, such as the Olifants, Upper Vaal, Inkomati, 
Thukela and Usutu-Mhlathuze, with the largest area located in the Upper Vaal catchment. The 
Highveld coalfield covers parts of the Olifants and Upper Vaal catchments. 
 
Figure 3.22: Elevation image of the study area showing the drainage pattern and rivers 
61 
 
 
The topographic slope for the study area varies between 0 and 121% (Figure 3.23) with the largest 
part of the area being flat, characterised by slopes below 5%. The southern portion, corresponding to 
the Majuba Mountains around the Volksrust area, is marked by very steep terrain.  
 
Figure 3.23: Topographic slope image of the study area 
3.4.5.2 Sources of ligands (water) 
In the study area, the sources of ligands used was the average long-term rainfall which was obtained 
from historical data published by the South African Weather Services (SAWS, 2016). Figure 3.24 
shows the average long-term rainfall which ranges between 634 and 1 045 mm and increases in a 
southeasterly direction. Most popular groundwater vulnerability assessment approaches (e.g. the 
DRASTIC method) use recharge values as a parameter that represents the transportation of pollutants. 
In this research where a specific groundwater vulnerability approach is being developed, average 
62 
 
 
long-term rainfall will be used as it captures both the availability of water for AMD reactions and 
availability of water (ligands) for the transportation of pollution from the surface to the groundwater. 
 
Figure 3.24: Average long-term rainfall of the study area 
In order to verify whether if the average rainfall is correlated with recharge data, regional recharge 
data from Department of Water and Sanitation (DWS) were used. 
The DWS conducted a study to generate a groundwater recharge map for South Africa at 1 km by 
1 km grid cell size (DWS, 2006). The method used to produce the recharge map is GIS-based and 
Quaternary catchments were used as the unit of measure. The recharge method essentially comprises 
four main components: 
• the Chloride Mass Balance (CMB) approach; 
• empirical rainfall/recharge relationships; 
63 
 
 
• layer model (GIS based) approach; and then 
• cross calibration of the results with field measurements and detailed catchment studies. 
The results obtained from the recharge study by the DWS were in agreement with results obtained 
from earlier recharge studies (DWS, 2006). Though the approach did not differentiate between 
preferred path and matrix diffusion recharge, it is GIS-based, making it sufficiently flexible to include 
updates and new datasets. Figure 3.25 shows the recharge map of the study area as extracted from the 
countrywide recharge map of South Africa. In the study area, high recharge areas (over 77 mm) are 
found in the eastern and south-eastern parts of the study area. The central and western parts of the 
study area are marked by lower recharge values (below 37 mm). 
 
Figure 3.25: Recharge image of the study area 
64 
 
 
The net recharge data covering the study area was plotted against average long-term rainfall and the 
results presented as a scatter plot, shown in Figure 3.26. A correlation coefficient value (	) of 0.821 
was obtained showing a strong positive correlatio	n! between net recharge values and average long-term rainfall. The coefficient of determination ( ) of 0.6741 shows that ~ 67% of the rainfall 
parameter contributes to the recharge (Figure 3.26). 
 
Figure 3.26: Relationship between average long-term rainfall and net recharge 
The usage of rainfall data which is highly correlated with recharge would ensure that the vital 
transport mechanisms are captured in the modelling. Using rainfall as a parameter would also reduce 
parameter dependencies which affect methodologies such as the DRASTIC methods. 
3.4.5.3 Surface sources of AMD pollution 
For the Witbank, Ermelo and Highveld coalfields, remote sensing (Landsat 8 and Sentinel 2) was 
used to identify secondary iron-bearing minerals which are produced by AMD formation reactions. 
The advantage of using orbital remote sensing data is that very large areas can be mapped at a 
relatively low cost and that most sources are mapped at the spatial resolution of the remote sensing 
data. 
3.4.5.3.1 Methodology for identification of AMD surface sources 
This section, based on a peer-reviewed conference publication (Sakala et al., 2017b) written as part 
of this research, was presented at the 13th International Mine Water Association Congress in 
Lappeenranta, Finland.  
65 
 
 
The methodology for the identification of AMD sources from Landsat 8 remote sensing data involves 
the following process flow: 
• Identification of the spectral signature of iron-bearing minerals in mine discard dumps within 
the study area. Identification can be done by taking several spectral readings of the mine 
discard dumps using a handheld spectroradiometer or extracting spectral data from 
publications from, for example, the USGS mineral spectral library (Swayze et al., 2000). The 
iron-bearing minerals are often indicators of the geochemical environment in which they were 
formed. The commonly known Fe-bearing minerals which are sensitive indicators of pH, Eh, 
relative humidity, degree of oxidation and other environmental conditions are copiapite (Fe+2 
Fe +34 (SO4)6(OH)2∙20(H2O)), jarosite (KFe +33 )(SO4)2(OH)6), schwertnannite 
(Fe +316 )O16(SO4)2 (OH)12∙nH2O(n~10 to 12)), ferrihydrite (5Fe2O3∙9H2O), goethite 
(Fe+3O(OH)) and haematite (Fe2O3) (Swayze et al., 2000; Crowley et al., 2003). Within the 
study area, the Fe-bearing minerals which form in abundance are haematite and jarosite, 
according to a study by Cole et al. (2015). The spectral uniqueness of these Fe-bearing 
minerals makes it possible to identify them from orbital and airborne imaging data. 
• Resampling of the mineral spectral data to remote sensing data, i.e. Landsat 8 and Sentinel 2 
bandwidth sizes in this study. 
• Comparison of various bands and identification of the reflectance value differences to be used 
in order to differentiate between the AMD indicator minerals and the other minerals present. 
• Developing a decision tree for differentiating various minerals using their reflectance 
responses at various bandwidths. The decision tree is then applied to the Landsat 8 and 
Sentinel 2 data to produce maps showing the distribution of the AMD indicator minerals. 
• Verification of the results by follow-up ground investigations over the identified AMD 
sources or onscreen verification on Google Earth images. 
In this study, free Landsat 8 and Sentinel 2 data downloaded from the USGS and Copernicus websites 
respectively were used to identify secondary iron-bearing minerals. Landsat 8 data comprise nine 
bands in the visible and near-infrared (VNIR) and short-wave infrared (SWIR) ranges (Band 8 is the 
panchromatic band and Band 9 is a cloud detection band) and two bands in the thermal infrared (TIR) 
range (Table 3.2). 
66 
 
 
Table 3.2: Properties of Landsat 8 data (Cole et al., 2015) 
 
Sentinel 2 data comprise 13 spectral bands in the VNIR and SWIR spectral range as shown in Table 
3.3. 
Table 3.3: Properties of Sentinel 2 (Satellite Imaging Corporation., 2017) 
 
The data are pre-processed by doing atmospheric correction and converting the Digital Number (DN) 
into reflectance values using QGIS automatic pre-processing modules. Clouds, cloud shadows and 
vegetation are masked out of the reflectance data to obviate the creation of false classification when 
running the minerals mapping process. The spectral signatures of all the secondary iron-bearing 
minerals can be extracted from the USGS spectral library (Clark et al., 2007).  
67 
 
 
The spectral signatures of copiapite, goethite, hematite, jarosite, ferrihydrite and schwertmannite 
from the USGS spectral library reveal that these six minerals show unique reflectance signatures 
which can be used to distinguish them from other minerals (Figure 3.27). 
 
Figure 3.27: Spectral signatures of iron-bearing minerals extracted from the USGS spectral 
library 
The spectral signatures of all the Fe-bearing minerals were resampled to the detection ranges of 
Landsat 8 and Sentinel 2 bands. The resampled spectral signatures of the six minerals (copiapite, 
goethite, hematite, jarosite, ferrihydrite and schwertmannite) still show their distinct spectral 
signatures on Landsat 8 and Sentinel 2 spectrum, as is evident from Figure 3.28 and Figure 3.29 
respectively. The spectral uniqueness of these Fe-bearing minerals makes it possible to identify them 
from orbital and airborne imaging data. Hence, only these minerals will be identifiable from the 
remote sensing data. 
  
Figure 3.28: Secondary iron minerals spectrum resampled to Landsat 8 bandwidths 
68 
 
 
 
Figure 3.29: Secondary iron minerals spectrum resampled to Sentinel 2 bandwidths 
An examination of the mineral spectrum which has been resampled to Landsat 8 (Figure 3.28) 
bandwidth, shows that the reflectance value for band 4 is greater than that of band 5 and that the 
reflectance value band 9 is greater than that of band 6. This is the spectral uniqueness of jarosite when 
compared with other secondary iron minerals which may be found in an acid environment. For 
haematite, the spectral uniqueness on Landsat 8 data is such that the reflectance value for band 5 is 
greater than that of band 4; the reflectance value for band 7 is greater than that of band 6 and the 
reflectance value of band 9 is greater than the reflectance value for band 6 (Figure 3.28). This spectral 
uniqueness of these minerals was used to create a decision tree to identify these minerals using 
Landsat 8 reflectance data. 
Sentinel 2 data has many bands which makes it easy to differentiate the minerals within a 10 m pixel 
sized grid cell. For jarosite, the spectral uniqueness on Sentinel 2 data is such that the reflectance 
value for band 11 is greater than that of band 12, the reflectance value for band 5 is greater than that 
of band 4, the reflectance value for band 8 is greater than that of band 9 and the reflectance value for 
band 10 is greater than that of band 11 (Figure 3.29). For hematite, the spectral uniqueness on Sentinel 
2 data is such that the reflectance value for band 12 is greater than that of band 11, band 11 is greater 
than the reflectance value for band 10, the reflectance value for band 9 is greater than that of band 8, 
the reflectance value for band 7 is greater than that of band 7 and the reflectance value for band 6 is 
greater than that of band 5 (Figure 3.29). 
69 
 
 
Using the observed spectral uniqueness of the two minerals, decision trees for Landsat 8 and 
Sentinel 2 were produced and are presented in Figure 3.30 and Figure 3.31 respectively. The decision 
tree was implemented in ArcGIS and the AMD-related secondary iron-bearing zones were identified. 
 
Figure 3.30: Decision tree used to identify secondary Fe minerals from Landsat 8 data 
 
Figure 3.31: Decision tree used to identify secondary Fe minerals from Sentinel 2 data 
70 
 
 
3.4.5.3.2 Results and discussions 
Not all mine residue dumps or coal discard faculties are acid generating. Only those that are indeed 
acid generating will precipitate the secondary iron minerals and thus be identifiable using this 
approach. After implementing the decision tree in a GIS environment: Landsat 8 and Sentinel 2 data 
covering the whole study area were used to produce maps showing only the interpreted Fe-bearing 
minerals which can be used as potential AMD surface sources. 
Figure 3.32 shows the interpreted Fe-bearing minerals (jarosite, hematite) extracted from Landsat 8 
data and the results are presented as a function of distance (Euclidean distance) from the pixel that is 
interpreted to contain these minerals. The Euclidean distance which is an “ordinary” straight-line 
distance between two points in the Euclidean space (Michel and Elena, 2009) was implemented in 
ArcGIS software using the Spatial Analysist tool. 
The Euclidean distance (=0) between points = and 0 on a map is the length of the line segment 
between them. In the Cartesian coordinates, if = =  =
, =!, … , =M) and 0 =  (0
, 0!, … , 0M) are two 
points in Euclidean n-space, then the distance () from = to 0, or from 0 to =, is given by the 
Pythagorean formula (Equation 3.3). 
(=, 0) = (0, =) =  NM
(0 − =)! 3.3 
The Witbank coalfields are marked by the highest density of the interpreted Fe-bearing minerals while 
the Ermelo and Highveld coalfields are marked by low densities where the minerals are only patchily 
located throughout the coalfields. 
71 
 
 
 
Figure 3.32: AMD surface sources as interpreted from Landsat 8 remote sensing data 
Figure 3.33 shows the interpreted Fe-bearing minerals (jarosite, hematite) extracted from Sentinel 2 
data respectively and results presented as a function of distance from the pixel that is interpreted to 
be having these minerals. Similarly, to the Landsat data, the Euclidean distance was implemented in 
ArcGIS software. The results from interpretation of Fe-bearing minerals on Sentinel 2 data show 
more pixels with these minerals compared to the Landsat 8 results. This could be because the 
Sentinel 2 data have more bands which define the absorption features of jarosite and hematite, hence 
the resolution of detection of these minerals is greatly improved. Also, the grid cell size of Sentinel 2 
data is smaller than that of Landsat 8 data which means that more pixels can be classified better 
without spectral mixing which is attributable to the classification of a larger grid cell size. 
72 
 
 
 
Figure 3.33: AMD surface sources as interpreted from Sentinel 2 remote sensing data 
The results from Landsat 8 and Sentinel 2 were combined using the logical “AND” operator to 
generate one combined interpretation map (Figure 3.34). The logical “AND” operator was chosen 
because minerals should appear on pixels of both the Landsat 8 and Sentinel 2 datasets. The logical 
“AND” output results which fuse the two datasets show that the Witbank coalfield is marked by the 
highest density of the secondary iron-bearing minerals while the Ermelo coalfield has the lowest 
density. A small section (black polygon in Figure 3.34) of the Witbank coalfield, where the density 
of pixels is highest was selected for a detailed analysis of the results. Another area (light blue polygon 
in Figure 3.34) where previous sampling had been done was also selected for comparison with the 
results of remote sensing interpreting. 
Using the area within the black polygon in Figure 3.34, the interpreted jarosite and hematite minerals 
are shown in red in Figure 3.35a. The area lies south of eMalahleni (black polygon in Figure 3.34) 
73 
 
 
and covers the Kendal, Ogies, Minnaar and Coalville areas (Figure 3.35a). When the interpreted 
results are overlain onto the Landsat 8 band 764 combination, it is clear that the mapped jarosite and 
hematite minerals coincide with some mine discard areas and coal loading terminals (Figure 3.35b). 
 
 Figure 3.34: Combined results from Landsat 8 and Sentinel 2 results plotted as a function of 
distance from interpreted AMD surface sources. The areas within the two black 
polygons are selected for detailed analysis  
The interpretation of the hyperspectral survey results covering the active coal mining areas of the 
Witbank coalfield (Cole et al., 2015) identified most mine discard dumps as potentially acid 
generating. The approach used in this research are in agreement with these findings and with the 
finding that several mine discard dumps around Ogies, Minnaar, Coalville and Kendal consisting of 
secondary iron-bearing minerals (represented in red in Figure 3.35) can be used as proxy as 
potentially acid generating phenomena. 
74 
 
 
 
Figure 3.35: Zoomed-in results (a) Iron-bearing minerals: (b) Landsat 8 band combination 
764 for a detailed analysis of interpreted secondary Fe minerals 
Several mine discard dumps in the Witbank coalfield which were identified as acid generating in a 
study conducted by Novhe et al. (2013) correspond to the mapped jarosite and hematite minerals. 
This finding is in agreement with the literature which states that the Witbank coalfield currently is 
the highest producer of coal while the Ermelo coalfield is the lowest (Bell et al., 2001; Hobbs et al., 
2009). 
To test the validity of the identified AMD sources, Novhe et al. (2013) compared the mine discard 
dumps classified as AMD sources with the dumps identified as acid generating by. Novhe et al. (2013) 
used static tests including paste pH, a neutralisation analysis, acid potential determination and kinetic 
tests (column leach tests) to identify AMD generating mine discard dumps in the Witbank coalfield. 
Consequently, the Arnot North Mine discard dump was identified as acid generating. The dump is 
characterised by high secondary Fe-bearing minerals (Figure 3.36). The results from the remote 
sensing technique are in agreement with these laboratory tests, thus increasing confidence in the usage 
of remote sensing data. 
75 
 
 
 
Figure 3.36: Zoomed-in results for Arnot North discard mine dump 
A selection of secondary Fe-bearing minerals based on aerial remote sensing data ensured that most 
of these minerals occurring in waste rocks and mine dumps and those that have been transported and 
deposited on roads, railway lines, loading bays, wetlands and river banks are all mapped at 30 m 
resolution. The mapped AMD pollutant sources can be used as an input to an AMD specific 
groundwater vulnerability assessment. 
3.4.5.4 Subsurface sources 
In the study area, the Ecca Group is known to generate AMD. The rock formation consists of 
sandstone, shale and pyrite-rich coal seams covering over 50% of the Witbank, Ermelo and Highveld 
coalfields. In this research, the Ecca Group rocks extracted from the 1:250 000-scale geology were 
considered as proxy for potential subsurface sources of AMD pollution (Figure 3.37). 
The subsurface sources are mainly found between the central and the northern part of the study area 
covering the northern parts of Highveld and Ermelo coalfields and the entire Witbank coalfield. 
3.4.5.5 Transport and attenuation in the soils 
The study areas is found in the main Karoo basin where the amount of soil clay content is considered 
to be of the important geological/hydrogeological factors which should be used for a groundwater 
vulnerability assessment (Woodford and Chevallier, 2002). 
76 
 
 
 
Figure 3.37: Subsurface AMD sources as interpreted from geology data 
In this study, only the soil clay content was used as a proxy for the transportation pathway and 
chemical traps in the soils. Soil data covering the study area at a scale of 1:250 000 were obtained 
from the Agricultural Research Council Institute for Soil, Climate and Water (ARC-ISCW). The soil 
types found in the study area range from freely drained apedal, plinthic catena, duplex, Glenrosa and 
Mispah (Figure 3.38). 
The Witbank coalfield is mainly covered by plinthic catena red soils, with small patches of Duplex 
and freely drained apedal soils. Almost the entire Highveld coalfield is covered by undifferentiated 
Duplex soils. Red plinthic catena, freely drained soils are also found in the northern part of the 
Highveld coalfield and small exposures of undifferentiated plinthic catena, Glenrosa and Mispah are 
found in the south. The Ermelo coalfield is covered by many soil types, ranging from red plinthic 
catena in the north to Duplex, plinthic, freely drained soils in the centre and small patches of Glenrosa 
and Mispah soils in the southern to eastern parts of the coalfield. 
77 
 
 
 
Figure 3.38: Soil types found in the study area 
These different soil types are characterised by varied clay content. Table 3.4 shows the various soil 
types found in the study area with their associated clay content. 
In the study area, the soil clay content varies between 9.9 and 51.2% (Figure 3.39). The Witbank 
coalfield is characterised by soils with a low clay content and thick soil cover. Conversely, the central 
part of Highveld and Ermelo coalfields is marked by high clay content. 
The soil CEC values which can be used as a meaningful surrogate for the overall attenuation processes 
in soils are a function of clay content and organic content. For the Witbank, Ermelo and Highveld 
coalfields, no high-resolution organic matter in soil data could be found, hence only the soil clay 
content will be used. 
In order to establish whether various soils with different clay contents have an influence on 
attenuation (traps) on AMD pollution, laboratory batch leach experiments were conducted. 
78 
 
 
Table 3.4: Soil types found in the study area and their associated estimated clay content 
 
 
Figure 3.39: Distribution of soil clay content within the study area showing the locations of 
soil samples collected for the chemical traps experiment 
79 
 
 
3.4.5.5.1 Materials and methods 
The experimental procedure for the batch leach experiment to study the chemical effects of soils on 
AMD pollution involved the following steps: 
1. Ten soil samples with distinct soil parameter values (soil clay content, soil CEC, soil organic 
matter, soil pH), based on the regional soil map (ARC-ISCW, 2015) of South Africa, were 
collected from various locations within the study area. The locations of the sampling points on 
the soil clay content map of the study area are shown as dark green stars in Figure 3.39. Mine 
water from an abandoned collapsed underground mine which is now decanting AMD was used. 
The chemistry of the mine water is shown in Table 3.5. 
2. The soils were air dried, crushed and sieved down to below the 2 mm particle size. Twenty 
grams (20 g) of the soil samples was weighed and transferred into 20 high-density polyethylene 
(HDPE) plastic bottles. Then 400 ml of AMD solution was transferred into ten of the bottles 
containing the soil samples. In view of control purposes and to provide the background values 
of the leachate unaffected by AMD, 400 ml of de-ionised water was transferred into the other 
ten bottles of soil samples. The 20 bottles were then loaded onto an automatic shaker and run 
for 48 hours as shown in Figure 3.40. 
3. After 48 hours, the leachate was collected and tested for pH and electrical conductivity (EC) 
and filtered prior to chemical analysis using the ICP-MS/DA and discrete analyser techniques. 
Full analyses can be found in Appendix 1.1 and 1.2. 
4. An XRF elemental composition analysis of the samples was done with the overall objective of 
understanding the mineral composition of each sample in support of the interpretation of the 
resulting leachate chemistry. A water chemistry analysis was done by checking the effect of 
soils on various AMD parameters such as pH, Fe, Al, SO4, Ca, Mg, Cl and Na. 
The actual laboratory setup is shown in Figure 3.40 and the properties of the soils used for the 
experiment are presented in Table 3.6. 
80 
 
 
Table 3.5: Chemical composition of AMD used for the soil batch leach experiment 
 
 
Figure 3.40: Experimental setup for determining the attenuation effect of soils on AMD 
pollution 
A scatter plot between soil clay content and regional CEC data (Figure 3.41) was generated for the 
ten sample locations 	and the results are displayed in Figure 3.42. The scatter plot shows a very strong positive correlation ( ) va	lu!e of 0.856 between soil clay content and regional CEC values. The fitted regression line (red line) (  = 0.7326) shows that the clay parameter accounts for ~73% of the CEC 
value. This is in agreement with findings by Lambooy (1984) who also observed a strong positive 
correlation between the clay content and the CEC for many South African soils. Thus, the soil clay 
content can be used as a proxy for traps in the soils. 
81 
 
 
Table 3.6: CEC, pH and clay content of the soil samples used in the batch leach experiment 
 
 
Figure 3.41: Soil CEC map of the study area 
82 
 
 
 
Figure 3.42: Scatter plot between soil CEC and soil clay content 
3.4.5.5.2 Experimental results and discussion 
After completing the batch experiment, the resulting chemistry of the leachate was analysed to 
establish whether clay content can be used as parameter for the chemical attenuation of AMD 
pollutants in the soils found in the Witbank, Ermelo and Highveld coalfields. 
Figure 3.43 shows the XRF elemental oxide analysis of the ten soil samples collected within the 
Witbank, Ermelo and Highveld coalfields. The order has been rearranged according to clay content 
to facilitate visualisation. It is evident that soils with a higher clay content are associated with the 
presence of elemental oxide of MgO and CaO and low SiO2. Full analysis can be found in 
Appendix 1.3. 
 
Figure 3.43: XRF Mineralogical composition of the soil samples 
83 
 
 
Iron 
Figure 3.44 shows the effect of introducing AMD to soils under laboratory conditions with reference 
to the original iron (Fe) concentration of AMD water and de-ionised water which was used as a 
control from which background leachate values can be compared. 
 
Figure 3.44: Plot of soil clay content against iron (Fe) leachate concentration. The red line 
marks the initial Fe concentration of the AMD. The blue and black points are 
leachate concentration values resulting from the effect of adding de-ionised water 
and AMD to soils respectively 
If soils have no influence on the Fe concentration of AMD after being its addition, then the Fe 
concentration in the resulting leachate would remain almost unchanged. However, from the fitted 
regression line (black line in Figure 3.44) a change in Fe concentration is noticeable where soils with 
high clay content show a slight reduction in the Fe concentration by over 20 mg/L in the 24 hour 
experimental period. However, no significant change in Fe concentration was observed for soils with 
a lower clay content. A possible explanation for the effect of the clay content on Fe concentration can 
be deduced by comparing the elemental oxide of soils with a high clay content and those with a lower 
content. The XRF results show that soils with high clay content (ES07/, 'ES02, ES09 and ES10) also contain a slightly higher amount of exchangeable bases (calcium as  and magnesium as E(') 
which could be displaced by Fe. Soils with a high clay content have more cation exchange sites which 
are initially occupied by MgO and CaO, but after addition of AMD, the pH lowers and Fe, which is 
very soluble at low pH, probably displaces the Mg+2 and Ca+2 from the exchange sites. The Fe 
concentration remained unchanged in soils with a lower clay content, meaning that no Fe is removed 
at a lower clay content as there will be fewer cation exchange sites available to extract the Fe ions 
from the AMD solution. 
84 
 
 
Aluminium 
No significant change in the Al concentration was observed as can be seen by the fitted regressing 
line which almost plots on the raw AMD water line (Figure 3.45). This probably shows that at low 
pH, Al is the main preferred ion that holds strongly on the soil exchangeable sites and is not easily 
replaced by any ion, accounting for the lack of change in the observed Al concentration. 
 
Figure 3.45: Plot of soil clay content against Aluminium (Al) leachate concentration. The red 
line marks the initial Fe concentration of the AMD and the blue and black points 
are leachate concentration values resulting from the effect of adding de-ionised 
water and AMD to soils respectively 
Sulphate 
The blue points in Figure 3.46 show that the sulphate (SO -24 ) concentration of leachate after batch 
reaction with de-ionised water is very low (<10 mg/L) compared to the leachate SO -2 4 concentration 
produced after adding AMD to soils of varied clay contents. When AMD is added to the soils, the 
SO -2 4 concentration decreases slightly with increasing clay content but is in the same order of 
magnitude. This may mean that the effect on SO -2 4 concentration is not too pronounced across soils 
of varied clay content. This can also be seen by the regression line (black line in Figure 3.46) plotting 
very close to the raw AMD line. The decrease in SO -2 4 concentration in the leachate with increasing 
clay content could be explained by the fact that soils with a high clay content have a strong ionic bond 
which prevents the mobilisation of SO -24  into solution. At a low clay content, the ionic bonds are 
weaker and results in the desorption of SO -24  ions into solution, resulting in an increase in the SO -24  
concentration. This relationship between SO -2 4 concentration and clay content was also observed by 
Tabatabai (1987). 
85 
 
 
 
Figure 3.46: Plot of soil clay content against Sulphate (SO -24 ) leachate concentration 
Thus, the soils were unable to attenuate SO -2 4 significantly in AMD conditions to which they had 
been subjected. In addition, the SO -2 4 concentration remained almost constant across all clay content 
values within the ranges of the ten samples. This may mean that SO -2 4 is slightly conservative across 
soils of varied clay content. Translating these findings to groundwater vulnerability, it appears that, 
irrespective of the clay content value of the soil, sulphates will pass through the soils with very little 
chemical attenuation. Thus, this property of SO -2 4 makes it a possible natural tracer of AMD pollution. 
Magnesium and calcium 
For soils with a clay content greater than 31%, magnesium (Mg) and calcium (Ca) ions are released 
in solution when AMD is added to soil in the batch leach experiment. This is reflected by an increase 
in Mg (Figure 3.47) and Ca (Figure 3.48) concentrations above the original concentration of AMD. 
This could be because these exchangeable bases were involved in ion exchange processes which 
liberated them into solution as observed by the increase in their concentration in the leachate. Below 
31% clay content, Mg and Ca concentrations remain unchanged after the batch leach experiment, as 
shown in Figure 3.47 and Figure 3.48 respectively. 
 
Figure 3.47: Plot of soil clay content against leachate Calcium (Ca) concentration 
86 
 
 
 
Figure 3.48: Plot of soil clay content against leachate Magnesium (Mg) concentration 
Sodium 
No change in the response of various soils in terms of sodium (Na+) concentration was observed, as 
reflected by the similarity in the response curves when soils are subjected to AMD and de-ionised 
water (Figure 3.49). The addition of AMD only increased the Na+ concentration by a factor which 
was preserved across all soil samples regardless of clay content. A possible explanation could be that 
Na+ ions did not partake in any exchange reactions during the time frame of the batch leach 
experiment. By considering the exchange affinity of Na+ ions (on Equation 3.4) in strongly acidic 
conditions such as that found in the batch experiment, Na+ is found at the edge of the list where the 
exchange sites are weakly held (Mani, 2014). 
),  O P*3,  Q /,!  Q E(,! Q R)-, =  , Q R/, 3.4 
Held more strongly Held more weakly 
 
Figure 3.49: Plot of soil clay content against leachate Sodium (Na) concentration 
87 
 
 
Summary 
In summary, the batch leach experiment revealed that soil clay content plays a role in attenuating of 
some of the pollutants found in AMD. Soils with a high clay content (greater than 31%) were able to 
reduce the concentration of iron and sulphates from the AMD as the leachate concentrations of 
magnesium and calcium increase. This could be explained by an exchange reaction where iron 
displaced magnesium and calcium from soil exchange sites. In the development of groundwater 
vulnerability specific to AMD at a coalfield, these experimental findings will be incorporated, where 
clay content will be used as proxy of the chemical attenuation of AMD by soils. 
3.4.5.6 Preferential pathways 
The information on regional faults was extracted from the 1:250 000-scale geology maps published 
by the Council for Geoscience and the lineaments (fractures, dyke) were interpreted from the regional 
airborne magnetic data and used as proxy for preferential pathways at a regional scale. Regional 
airborne magnetic data acquired at a height of 150 ± 15 metres above the ground with 1 km line 
spacing along an E–W direction was accessed from the Council for Geoscience geophysics database. 
Figure 3.50 shows the residual magnetic field intensity map with an interpretation of the lineaments 
and possible faults. 
Different processing techniques were applied to the magnetic data in order to achieve the objectives 
of mapping possible preferential pathways within the Witbank, Ermelo and Highveld coalfields. 
These techniques included the vertical derivative and analytic signal derived from the total magnetic 
intensity map of the area. The first vertical derivative and the analytic signal are high-pass filters 
which enhance lineaments and geological contacts at a shallow depth. The airborne magnetic data 
were interpreted to identify dykes, lineaments and magnetic source bodies that exercise some form 
of control over the migration of AMD pollutants in the subsurface. The magnetic anomalies range 
from dipolar (low–high) positive magnetic types to subdued and high linear anomalies. The subdued 
to high linear anomalies were interpreted as dolerite dykes and magnetic mineral-filled fracture zones 
(blue lines in Figure 3.50). 
 
88 
 
 
 
Figure 3.50: Residual magnetic field with lineaments and interpretations of the faults 
The dipolar (low–high) magnetic anomalies in the northern part of Highveld coalfield extending into 
the Witbank coalfield could be attributable to dolerite sills which are generally characterised by a 
high content of magnetic minerals compared to the surrounding sandstones and shales found in these 
coalfields (Figure 3.51). The analytical signal image clearly shows these sills to be very high-
amplitude anomalies. Faults were also interpreted as these features appear on magnetic maps as an 
abrupt break or the displacement of an otherwise continuous geological feature. Some appear as 
sudden truncation of geological features. No in-depth study to discern whether the linear anomalies 
are attributable to dykes or fractures was done because the effects of these geological features on 
groundwater pollution migration is the same, in that they both act as conduits that transport pollution 
from the surface to the groundwater. 
89 
 
 
 
Figure 3.51: Magnetic analytical signal showing the interpretation of the sills 
Figure 3.52 shows the combined interpretation of possible preferential conduits as mapped from 
regional magnetic data for the three coalfields. The interpreted sills are shown in gold and lineaments 
are represented by long lines blue lines. Faults, as interpreted from magnetic data, are represented by 
black dotted lines. 
90 
 
 
 
Figure 3.52: Magnetic interpretation of the possible preferential pathways 
These pathways interpretations were converted into a Euclidean distance, shown in Figure 3.53. The 
ArcGIS spatial analysist tool was used to generate the Euclidean distance which shows distance from 
the interpreted lineaments and sill boundaries. A high density of lineaments is found around the town 
of Ermelo and very few lineaments were interpreted in the southern part of the study area. 
91 
 
 
 
Figure 3.53: Possible regional preferential pathways for AMD represented as a distance map 
3.4.5.7 Rock permeability 
 For this study, rock permeability values were obtained from Wolff (1982) for all the different rock 
types found in the study area and used to produce a relative permeability distribution map (Figure 
3.54). The rock permeability of various rocks in the study area varies between 10-11 to 10-2 cm2 were 
expressed as relative values between 1 and 10, where 10 represents the rocks with the highest values 
and 1 represents those with the lowest values. 
92 
 
 
 
Figure 3.54: Rock permeability map generated from the literature, reflecting the values of the 
rocks found in the study area. Values in brackets are in cm2 
3.4.5.8 Hydraulic conductivity 
No pump testing was done in this research with the hydraulic conductivity values having been 
extracted from literature (Freeze and Cherry, 1979; Domenico and Schwartz, 1990; Barnard, 2000) 
for various rocks within the study area and assigned to each rock formation. The values for aquifer 
hydraulic conductivity ranges between 10-11 and 10-2 m/s and were expressed as relative values 
between 1 and 10, where 10 represents the rocks with the highest values and 1 represents those with 
the lowest values. Figure 3.55 shows the relative aquifer hydraulic conductivity values for various 
rocks. 
93 
 
 
 
Figure 3.55: Aquifer hydraulic conductivity map of the study area 
3.4.5.9 Depth to water table 
The water level data covering the study area was obtained from the South African Department of 
Water and Sanitation (DWS) National Groundwater Archive database where 4 927 boreholes with 
depth to water table values are recorded within the study area. The ArcGIS spatial analyst kriging 
technique was used to produce a depth to water table gridded map (Figure 3.56). The central part of 
the study areas covering both the Highveld and the Ermelo coalfields is characterised by a very 
shallow depth to water table. A depth to water table below 15 m is found in the northwestern part of 
the Witbank coalfield around Delmas. 
94 
 
 
 
Figure 3.56: Depth to water level map derived from monitoring borehole information from 
the Department of Water and Sanitation 
3.4.5.10 Rock-AMD reactivity 
In order to understand how AMD interacts chemically with various rocks found in the Witbank, 
Ermelo and Highveld coalfields, various laboratory experiments were conducted. The overall goal of 
the experiments was to study how AMD interacts with various rocks under the saturated and 
unsaturated conditions which typically prevail in the subsurface. Moreover, the tests focussed on 
clarifying the interactions between various rocks and the AMD ranking reflecting their ability to 
extract AMD pollutants and their buffering capacities. The results from the ranking of various rocks 
in terms of their ability to extract AMD pollutants would be used as an input to the SPT approach 
being developed in this research. The experiment attempted to mimic the natural attenuation of the 
subsurface with reference to rock-AMD interaction. Two column leach experiments for saturated and 
unsaturated conditions were set up for this study. 
95 
 
 
3.4.5.10.1 Materials and methods 
The experimental procedure for the rock-AMD interaction study involved the following steps: 
1. Fifteen representative fresh rock samples weighing 5–8 kg per sample were collected from 
various outcropping major lithologies and one sample was collected at a coal mining waste rock 
dumping site within the Witbank, Ermelo and Highveld coalfields. The rock samples were 
milled and sieved to below 2 mm particle size. A full mineralogical analysis of the samples was 
done with the overall objective of understanding the mineral composition of each sample and 
selecting five classes representing the general mineral distribution of the whole coalfield area. 
Although reducing the sample sizes statistically would increase the error when dealing with 
spatial distribution over a large area, financial constraints dictated the restriction of the number 
of samples to five. 
2. Mineral and elemental analyses using XRF, XRD and petrographic examination were carried 
out on the 15 samples. The results will be discussed and a justification of selection of the five 
samples given. 
3. After selecting five samples for the column leach test, each sample was split into two for two 
experiments (saturated and unsaturated). Then, the samples were fed into separate columns, thus 
amounting to a total of five columns for the saturated and five columns for the unsaturated 
conditions. Figure 3.57 presents a schematic diagram of the setup of the columns for the 
saturated and unsaturated experiments. 
4. The saturated column test was set up as shown in Figure 3.57a, where AMD was introduced 
from the bottom and passed through the rock sample to ensure its complete submersion in AMD 
and the resultant leachate was analysed weekly until an appreciable comparison could be made 
between the various rocks samples. 
5. The unsaturated column test was set up as shown in Figure 3.57b, where AMD occasionally fed 
from the open top and passed through the rock sample react with the AMD in the presence of 
atmospheric air to mimic unsaturated conditions. The resultant leachate was analysed weekly 
until such time as an appreciable comparison could be made between the various rocks samples. 
6. Mine water used in the soil batch leach experiment was also used for the rock-AMD reactivity 
experiment. 
96 
 
 
 
Figure 3.57: Schematic laboratory setup for (a) saturated and (b) unsaturated column tests 
7. Originally, the experiment was designed to extract the mine waste material from a mine in the 
study area containing pyrite and to use it to generate AMD in the laboratory to be fed into each 
column. This plan was abandoned after realising that the output from the AMD generating 
column was variable for each of the AMD generating columns, a result that would complicate 
the subsequent interpretation of the reactions. The laboratory setup before modifications was 
made is shown in Figure 3.58. The section of the experiment highlighted by a yellow dotted line 
was replaced by a container of AMD which had been collected from a decanting abandoned 
underground mine in the Witbank coalfield. The chemical analysis of the AMD is shown in 
Table 3.5. 
8. The parameters for the actual experiment are as follows: column height – 45 cm, column 
diameter – 11 cm, crushed rock sample weight – 1.38 kg. The experiments were run for 90 days. 
The flow rate for the saturated experiment was maintained at 0.01 ml/min to ensure that the 
column was completely saturated while at the same time allowing enough time for the reactions 
to occur. 
9. The analyses of the leachate from the collection include: pH, TDS, EC, alkalinity, Al, Mn, SO 24 , 
Ca, Mg, Na, K, N, Cl and others using ICP-MS and IC analytical techniques. A full chemical 
97 
 
 
analysis can be found in Appendix 2.1 and 2.2 for saturated and unsaturated conditions 
respectively. 
10. The actual laboratory setup is shown in Figure 3.58. 
 
Figure 3.58: Experimental setup for determining the attenuation effect of vadose zone and in 
the aquifer system. The yellow section was replaced by AMD collected from the 
field 
3.4.5.10.2 Sample mineralogy results and discussions 
In the X-ray diffraction machine the samples were scanned from 2 to 70o 2b Bcd radiation and phase 
concentrations were determined as semi-quantitative estimates using relative peak height/area 
proportions. The results for the 15 samples were plotted on a bar graph in order to compare and 
classify the mineral compositions of the various rock samples. Sample WITS01 uniquely contained 
almost equal proportions of silicates, plagioclase, quartz and chlorite; thus, this sample was selected. 
A full XRD analysis can be found in Appendix 2.3. 
Samples WITS07 and WITS14 were composed almost entirely of quartz and dolomite respectively 
(Figure 3.59). These rocks are known to have almost opposite responses (Eary and Williamson, 2006) 
in an AMD environment. The 15 samples were also analysed for their elememtal composition using 
XRF. The results from the XRF analysis (Appendix 2.4) were plotted on a bar graph to facilitate 
visualisation and comparison. Figure  3'.60 shows that tPhe*  m'ost dominant elemental oxide for all the samples (except sample WITS14) is ! followed by ! 3. Other elemental oxides which showed 
98 
 
 
up prominently were E(' and /'. These elemental oxides which accounted for 10% or more of 
the composition of the samples, were found in samples WITS01, WITS09, WITS10, WITS11 and 
WITS14. The 15 samples were grouped into five groups according to their elememtal composition, 
as shown in Table 3.7. 
 
Figure 3.59: Mineral composition of various rocks as measured by XRD, showing the five 
selected samples for the column leach experiment 
 
Figure 3.60: XRF minerals composition of various rocks showing the five selected for the 
column leach experiment 
99 
 
 
Table 3.7: Groups of samples according to their mineral speciation as interpreted from XRF 
results 
 
The selected five representative samples (Table 3.7) were further analysed under a microscope to 
establish the spatial arrangement of their minerals in detail. 
Diabase (WITS1) sample: under the microscope, the sample section is dominated by medium to 
coarse-grained elongate crystals of plagioclase feldspar, with some wrapped around by strongly 
coloured varieties of augitic pyroxenes (clinopyroxene characteristic) crystals (Figure 3.61). 
Observation under the microscope identified the grain size of plagioclase to be in the order of 1.8 mm. 
 
Figure 3.61: Microscopic view of the medium to coarse-grained diabase showing elongated 
crystals of plagioclase feldspar (Sample WITS1) 
Sandstone (WITS7) sample: under the microscope, the sample section is dominated by medium to 
fine-grained quartz with some grains occurring as angular to sub-angular crystals while others are 
euhedral (Figure 3.62). Both kaolinite and mica appear as fairly fine-grained colourful crystals and 
develop as rims surrounding the quartz crystal boundaries. Under the microscope, the grain size of 
quartz is just under 0.68 mm. 
Pillow lava (WITS8) sample: under the microscope, the sample shows very fine-grained quartz 
minerals and feldspar crystals forming a clay-rich matrix around them (Figure 3.63). Feldspar occurs 
100 
 
 
as fine-grained crystals which make it difficult to precisely distinguish whether the section comprises 
plagioclase or sanidine or both. Alteration phases observed in the section include chlorite which 
occurs with clay minerals such as kaolinite. Lamination was also observed. 
 
Figure 3.62: Quartzitic sandstone with lithic fragments as seen under the microscope for 
sample WITS7 
 
Figure 3.63: Very fine grains of quartz and feldspar as seen under the microscope for sample 
WITS8 
Hornfeld (WITS 9) sample: the microscopic section of this rock sample is dominated by fine- to 
coarse-grained randomly oriented laths of plagioclase which generally exhibit lamella twinning 
(Figure 3.64). The plagioclase laths generally occur in localised clusters with interlocking grain-to-
grain boundaries. A fine- to medium-grained patch of pyroxene, which appears to be predominantly 
clinopyroxene, occurs interstitially with the plagioclase laths. Clinopyroxene patches locally enclose 
laths of plagioclase subophitically. Large patches of plagioclase that appear to have been altered to 
sericite were also recorded scattered throughout the section. Patches of smectite, which appear to 
101 
 
 
have been derived from the alteration of clinopyroxene, are also present. Under the microscope, the 
grain size of plagioclase is just under 3.15 mm. 
 
Figure 3.64: Plagioclase laths ophitically to sub-ophitically enclosed in clinopyroxene, as seen 
under the microscope for sample WITS9 
Dolomite (WITS 14) sample: the microscopic section of this rock sample is dominated by fine-
grained tightly packed anhedral crystals of calcite and dolomite (Figure 3.65). The dolomite crystals 
appear transparent, cloudy to dark in colour. Calcite has high birefringence; its colour with crossed 
polars shows distinctive rainbow colours of pink and green flashes. This section reveals dolomite and 
calcite presenting a mosaic of fine-grained crystals with poorly defined, non-planar boundaries. The 
section also shows clinopyroxene crystals occurring with dolomite and calcite. 
 
Figure 3.65: Very fine-grained calcite and dolomite predominate in sample WITS14, as seen 
under the microscope 
102 
 
 
3.4.5.10.3 Experimental results and discussion 
Leachate samples were collected on a weekly basis and analysed for major, minor and trace elements, 
but only results for pH, iron (Fe), sulphate (SO4), aluminium (Al), manganese (Mn), calcium (Ca), 
sodium (Na) and magnesium (Mg) against time in days were presented as graphs. The graph (Figure 
3.66) shows the neutralising capacity of various rocks in an AMD environment under saturated 
conditions at room temperature in the laboratory. 
 
Figure 3.66: Graphic plot of leachate pH against time for various rocks under saturated 
conditions 
pH 
When AMD was reacted with different rock samples containing different minerals, different pH 
changes were observed, as shown in Figure 3.66. Sample WITS14 raised the pH from an initial 2.8 
to near-neural (around 7 to 8) from the seventh day until the end of the sampling period. The sample 
is made up of dolomitic carbonate minerals which react and change the pH to a neutral condition. 
Then other rock samples (WITS1, WITS7, WITS8 and WITS9) showed a minor change in the pH of 
the AMD. 
A small increase in pH was recorded for the other rock samples (WITS1, WITS7, WITS8 and WITS9) 
after the first week before the pH returned back to around 2.8. Sample WITS7 showed the least 
neutralisation capacity as it is composed of over 90% quartz and therefore lacked the ability to 
neutralise pH within the time frame of the experiment. Despite the little change in pH for the other 
rock samples, a buffering order (from high to low) can be deduced in term of neutralisation capacity 
under saturated conditions in the laboratory as follows: 
WITS14 > WITS1 > WITS9 > WITS8 > WITS7 
Figure 3.67 shows the neutralisation capacity of various rocks under unsaturated conditions at room 
temperature and pressure. The graph clearly shows that WITS14 buffered the pH from 2.8 to a pH of 
around 8 from the seventh day until the end of the experiment. The carbonate minerals found in the 
dolomite accounted for the neutralisation. An increase in neutralisation of the other rocks was 
recorded when the rock and AMD reacted under unsaturated conditions, probably as a result of the 
effect of the presence of oxygen on the kinetics of reactions. Sample WITS 1 raised the pH from 2.8 
103 
 
 
to neutral from the seventh day until the 29th day, when neutralising capacity was lost and the leachate 
pH returned to acidic conditions of around pH 4. Sample WITS 9 also neutralised the pH but the 
effect was short lived lasting only eight days, after which the pH returned to an acidic condition of 
around 3.5. Little change in pH was observed for WITS8, with the pH remaining acidic at a value of 
below 5. No pH buffering was recorded for sample WITS7. The pH neutralisation in unsaturated 
conditions is similar to that observed for saturated conditions and follows the order: 
WITS14 > WITS1 > WITS9 > WITS8 > WITS7 
 
Figure 3.67: Graphic plot of leachate pH with time for various rocks under unsaturated 
conditions 
The difference between the neutralisation capacity of various saturated and unsaturated rocks is very 
pronounced. This probably shows the role played by the presence of oxygen which caused the 
reactivity of some of the minerals to be increased. More research can be done by reactive modelling 
to establish why the kinetics are faster in reactions with oxygen than in those where oxygen is not 
present. 
Electrical Conductivity 
Figure 3.68 shows plots of the EC of leachate against time in days for various rock samples under 
saturated conditions. All the plots show a similar trend with regard to changes in EC with time where 
the EC values decrease until day 63 when a gradual increase in EC is observed until the end of the 
experiment. This trend can be attributed to the removal of minerals which make up the EC from 
solution by the rock mass. This removal is sustainable only for the first 63 days, after which the 
minerals are released back into solution. This accounts for the gradual increase in EC after 63 days. 
No clear order in terms of the reduction of EC could be established from the saturated conditions. 
104 
 
 
 
Figure 3.68: Graphic plot of leachate EC with time for various rocks under saturated 
conditions 
In unsaturated conditions, EC plots show a general decrease in EC values for the first 63 days of the 
experiment, after which a notable increase is observed (Figure 3.69). The order in which various rocks 
reduce EC is not very clear, but using results from day 21 to 78, the order of reduction is as follows: 
WITS1 > WITS8 > WITS9 > WITS14 > WITS7. The diabase sample, WITS 1, which consists of 
over 40% plagioclase feldspar, and the pillow lava sample (WITS 8) which consists of quartz, 
feldspar and chlorite were able to reduce the EC to below 3 000 µS/cm even though this result did 
not last longer than 63 days, after which the EC values started to increase. 
 
Figure 3.69: Graphic plots of leachate EC with time for various rocks under unsaturated 
conditions 
The sandstone sample (WITS7) consisting almost entirely of quartz showed the least decrease in EC. 
No noticeable effect with regards to EC was recorded for the dolomite (WITS14) and quartz (WITS7) 
in terms of decreasing the EC values. A slight decrease was observed for the hornfels (WITS9) 
samples. 
Sulphate 
Under saturated conditions, a noticeable decrease in sulphate concentration from 2 865 mg/L to below 
2 400 mg/L was observed for all the rock samples (Figure 3.70). This may be attributed to the initial 
removal of sulphate ions from the solution by the process of absorption of the negative ions onto the 
rock mass surfaces. This effect only lasted for 50 days when the sulphate ions were gradually released 
back into solution, thus increasing the concentration, as observed. The order of removal of the 
sulphate ions is not very clear for the saturated conditions. 
105 
 
 
 
Figure 3.70: Graphic plot of leachate sulphate concentrations over time for various rocks 
under saturated conditions 
A significant reduction in sulphate concentration from 2 865 mg/L to 2 400 mg/L was recorded in the 
first 20 days of the experiment (Figure 3.71) under unsaturated conditions. All the rock samples 
showed a similar change in leachate sulphate concentration over time. In terms of the reduction of 
sulphate concentration, samples WITS9, WITS7, WITS1 and WITS8 followed a similar trend and 
registered similar sulphate concentration values. 
 
Figure 3.71: Graphic plot of leachate sulphate concentration over time for various rocks 
under unsaturated conditions 
Dolomite sample WITS14 showed the least reduction of sulphate concentration. The order of sulphate 
reduction in the various rocks is not very clear but can be approximated as follows: 
WITS1 = WITS7 = WITS8 = WITS9 > WITS14. The sulphate plots for the various rocks are similar, 
showing that the geology does not affect sulphate removal or addition. Thus, sulphate movement is 
fairly conservative over various rocks within the time frame over which the experiment was 
conducted. 
Iron 
In terms of iron removal by various rocks, the order is not clear for saturated conditions. Nevertheless, 
it is noticeable that dolomite (WITS14) and pillow lava (WITS8) were able to reduce the Fe 
concentration to values below 40 mg/L for WITS 8 and below 1 mg/L for WITS14 (Figure 3.72). For 
unsaturated conditions, samples WITS1, WITS8, WITS9, WITS14 followed a similar trend where 
the iron concentration was decreased from 140 mg/L to very low values below 20 mg/L (Figure 3.73). 
A decrease in Fe concentration was recorded for sample WITS7, although the decrease was 
106 
 
 
significant and resulted in the lowest value recorded for all the rock samples. The order of iron 
reduction from solution can be approximated as follows: 
WITS14 > WITS1 = WITS8 > WITS9 > WITS7. 
 
Figure 3.72: Graphic plot of leachate iron concentrations over time for various rocks under 
saturated conditions 
 
Figure 3.73: Graphic plot of leachate iron concentration over time for various samples under 
unsaturated conditions 
Aluminium 
In the first seven days, WITS14 was able to reduce the concentration of aluminium (Al) to a very low 
value ~ 1 mg/L (Figure 3.74). For samples, WITS8 and WITS7, an increase in the Al concentration 
was observed. Under unsaturated conditions, dolomite (WITS14) was again observed to be able to 
reduce the Al concentration to below 1 mg/L (Figure 3.75). For the first 21 days, the Al concentration 
was reduced to very low values for samples WITS9 and WITS1. 
 
Figure 3.74: Graphic plot of leachate aluminium concentrations over time under saturated 
conditions 
107 
 
 
 
Figure 3.75: Graphic plot of leachate aluminium concentration over time for various samples 
under unsaturated conditions 
Sample WITS8 also showed a slight decrease in Al concentrations but the effect was short lived, 
lasting only a few days. The order in which each of the five samples reduced Al concentrations from 
the leachate may be summarised as follows: WITS14 > WITS1 > WITS9 > WITS8 > WITS7. 
Manganese 
A similar trend in the change over time in regard to manganese (Mn) concentrations in the leachate 
was observed for samples (WITS7, WITS8, WITS1 and WITS9) under saturated conditions. Sample 
WITS14 showed a reduction in Mn concentrations instead of a slight increase as was the case for the 
other samples (Figure 3.76). 
 
Figure 3.76: Graphic plot of leachate manganese concentrations over time for various samples 
under saturated conditions 
Figure 3.77 shows plots of Mn concentrations against time for the five samples subjected to AMD 
under unsaturated conditions. The plots show that the dolomite in sample WITS14 reduced the Mn 
concentration from solution in the first 47 days after which the Mn started to increase gradually until 
the end of the experiment. For sample WITS1, the Mn concentration only decreased to less than 
10 mg/L in the first 7 days after which it increased to over 50 mg/L before returning to the background 
value of around 30 mg/L. The order of reduction in Mn for the various rocks may be summarised as 
follows: WITS14 > WITS1 > WITS9 > WITS8 > WITS7. 
108 
 
 
 
Figure 3.77: Graphic plot of leachate manganese concentrations over time for various samples 
under unsaturated conditions 
Magnesium 
Figure 3.78 shows the change in magnesium (Mg) concentration in the leachate over the time period 
of the experiment under saturated conditions. In all the columns, there is a slight increase in Mg 
concentration in the first 7 days. The trend then flattens over the next 63 days, after which a sharp 
decrease to 40 mg/L is observed in all the columns. The greatest increase in Mg was recorded in the 
column with dolomitic material (WITS14) while the least change was observed for WITS07. 
 
 
Figure 3.78: Graphic plot of leachate magnesium concentrations over time for various 
samples under saturated conditions 
Figure 3.79 shows plots of Mg concentration versus time for the five samples subjected with AMD 
under unsaturated conditions. The plots show a similar trend as for the saturated conditions, probably 
implying that the availability of oxygen does not play a major role in the effect of AMD on various 
rocks in terms of magnesium concentration. 
109 
 
 
 
Figure 3.79: Graphic plot of leachate magnesium concentrations over time for various 
samples under unsaturated conditions 
Sodium 
Figure 3.80 shows the change in sodium (Na) concentrations in leachate over the time period of the 
experiment under saturated conditions. In all the columns, there was no change in Na concentration 
over the first 70 days of the experiment, after which a significant increase was observed in all the 
columns, with dolomitic sample (WITS14) showing the greatest change. The change occurred when 
the Mg concentration started to decrease from the leachate, probably reflecting an exchange reaction 
between Mg and Na, where Mg displaced Na into solution, causing its concentration increase in the 
leachate from the columns. 
 
Figure 3.80: Graphic plot of leachate sodium concentrations over time for various samples 
under saturated conditions 
Figure 3.81 shows plots of Na concentrations over time for various rocks which mimic unsaturated 
conditions. The results for Na concentrations show a similar trend as for saturated conditions, 
probably implying that the availability of oxygen does not play a major role in Na concentration in 
rocks subjected to AMD. 
110 
 
 
 
Figure 3.81: Graphic plot of leachate sodium concentrations over time for various samples 
under unsaturated conditions 
Calcium 
A plot of calcium concentrations obtained in the leachate from various columns plotted against time 
showed almost no change in Ca concentrations in all the samples, with the exception of WITS14. 
Leachate from column with WITS14 dolomitic samples showed an increase in Ca concentrations over 
the first seven days in response to the change in pH which had been observed over the same period. 
From the seventh day until the end of the experiment, the pH remained almost constant at near neutral 
~7.5 and the leachate Ca concentration remained high as well, probably showing the effect of pH on 
the leaching of Ca in solution. Similar trends in Ca concentration were observed for the unsaturated 
condition, as shown in Figure 3.83. 
 
Figure 3.82: Graphic plot of leachate calcium concentrations over time for various samples 
under saturated conditions 
 
Figure 3.83: Graphic plot of leachate calcium concentrations over time for various samples 
under unsaturated conditions 
111 
 
 
Chloride 
Rocks in the column tubes were subjected to AMD under saturated and unsaturated conditions and 
the chloride (Cl) concentrations of the resultant leachate were measured (Figure 3.84 and Figure 
3.85). It was discovered that the concentration of chloride remained almost unchanged over the time 
period of the experiment, probably reflecting the lack of effect in regard to Cl for all the reactions 
when rocks are subjected to AMD in either saturated or unsaturated conditions. Thus, Cl is 
conservative as it remains unchanged for the various rocks, maintaining the same concentrations over 
time regardless of pH conditions.  
 
Figure 3.84: Graphic plot of leachate chloride concentrations over time for various samples 
under saturated conditions 
 
Figure 3.85: Graphic plot of leachate chloride concentrations over time for various samples 
under unsaturated conditions 
Dissolution of Dolomite, Plagioclase, Quartz 
Research conducted in order to explain the results of the various columns in terms of the processes 
responsible for the nature of the leachate produced, showed that the dissolution of the various major 
minerals constituting each sample could be used. 
Dissolution of dolomite in the column with sample WITS14: when dolomite is the only available 
carbonate (as shown by the XRD results in the presence of oxygen and water-saturated conditions) 
neutralisation reactions occur according to Equation 3.5 as stated by Stumm and Morgan (1996) and 
Gomo and Masemola (2016): 
 ! + /E(('3)! + 3.75'! + 1.5)!' ↔ ('))3 + 2 '-.! + /,! + E(,! + 2'! 3.5 
112 
 
 
The dolomite AMD buffering r/eEac(ti(on' Eq)uation 3.5 conceptually shows t'hat when  ! from the AMD reacts with dolomite ( (')3) !) in the presence of oxygen ( !) and  w'a.ter ()!'), a hy/dr,o!xyl complex ofE ir(o,n! (III) ( 3) is prod'uced together with sulphates ( - !), calcium ( ), magnesium ( ) and carbon dioxide ( !). Based on this conceptual model, when such 
reactions occur, calcium and magnesium concentrations are likely to increase as was seen in the Ca 
and Mg plots for WITS14 under unsaturated conditions where both oxygen and water were present. 
At the same time, Fe concentrations decreased as free Fe ions form complexes which adhere to the 
mineral grains of the rock sample, thus accounting for the observed decrease in Fe concentration. The 
solubility of aluminium and manganese is pH dependent (Wright et al., 2001) when pH is neutral 
they precipitate and when pH is low they are in solution, as was reflected by the change in the leachate 
concentrations of these elements as pH changed from low to neutral (Figure 3.66 and Figure 3.67). 
Dissolution of plagioclase in column with sample WI TS'09:P b*a'sed, on t'he  X/R'F results (Figure 3.60), the most elemental oxides in the WITS09 sample are !, /P! * 3  '! 3 ; thus the chemistry of this sample was controlled by the dissolution of anorthite ( ! ! f) minerals. The dissolution of 
anorthite is a well-studied phenomenon and may be represented by Equation 3.6 given by Oelkers 
and Schott (1995): 
/P*! !'f + 8),  ↔ /,! +  2P*,3 +  2 '! + 4)!' 3.6 
Based on this conceptual understanding of Equation 3.6 representing the dissolution/ ,o!f anorthite which makes up sample WITS09, it can be seen that the dissolution reactions produce  and P*,3 
ions in solution. This was particularly noted when the dissolution reactions took place, as evidenced 
by the change in pH from acidic to near neutral accompanied by an increase in calcium concentrations 
Pfo*u,n3d in the leachate. However, the aluminium concentration did not increase in solution because the  ions formed complexes of hydroxyl which adhered to the grains of the rock material and were 
not found in solution, as may be seen by the low concentrations of the resultant leachate. 
D i'ssolution of quartz in the column with sample WITS07: sample WITS07 is made up of over 95% !, thus, the dissolution of silicate minerals can be used to explain the results of the leachate 
collected. The dissolution of silicate is a very slow process, even in an acidic environment (Kamiya 
et al., 1974). This explains why no significant change was observed for pH, sulphate, iron, aluminium 
and the manganese concentrations for the column with sample WITS07. 
3.4.5.10.4 Summary 
Based on the interpretation of the leachate concentration in relationship to the rock mineral 
composition for various rocks in the AMD environment, an approximate order of rock-AMD 
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reactivity can be deduced for the Witbank, Ermelo and Highveld coalfields. Table 3.8 shows a 
summary of the findings of the experiment. 
From the experiment it can be deduced that dolomite, which contains of 90% dolomitic carbonate 
minerals, was able to buffer the pH to neutral conditions which, in turn removed the heavy metals 
(Fe, Al and Mn) from the AMD solution. Diabase with medium- to coarse-grained elongate crystals 
of plagioclase feldspar which are aluminium complexes was also able to buffer the acidic conditions, 
but given that the buffering minerals are easily exhausted, buffering only lasted a few weeks. In terms 
of AMD extraction by rocks, hornfels follows diabase where the fine- to coarse-grained randomly 
oriented laths of plagioclase are responsive in buffering the acidic conditions and removing heavy 
minerals. The process is kinetically fast and only lasts a few weeks. Pillow lava, which is dominated 
by very fine-grained quartz and feldspar crystals, are also able to buffer the acidity to a lesser extent, 
but the process lasts a few days. Sandstones are the least effective in terms of buffering acidity and 
removing heavy metals (Fe, Al, Mn) from AMD solution. The sandstones are made up almost entirely 
of quartz minerals which lack the ability to buffer acidity or remove heavy metals in the time frame 
of the experiment. 
Table 3.8: Summary of rock–AMD reactivity expressed in terms of AMD removal by rocks 
 
Of particular interest is that hardly any rocks tested were able to remove sulphates under saturated 
and/or unsaturated conditions. Moreover, all the rock leachates were shown to follow an almost 
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similar pattern over time. Thus, sulphate may be considered conservative in both saturated and 
unsaturated conditions and can be used as a possible tracer for AMD pollution. Another interesting 
observation from the experiment is that pH buffering and metal removals were more pronounced in 
the unsaturated zone than in the saturated zone, probably as a result of the presence of oxygen. 
The results from the rock-AMD reactivity experiment were used as a guide to the classification of the 
rocks in the coalfields based on the mineralogical similarities between those rocks and the rock 
samples of the experiment. Table 3.9 shows the classification of various rocks found in Witbank, 
Ermelo and Highveld coalfields in terms of their reactivity in the AMD environment. 
Table 3.9: Summary of the rock-AMD reactivity for the Witbank, Ermelo and Highveld 
coalfields 
 
The rocks were assigned relative values from 1 to 10 according to their ability to buffer acidity and 
heavy metal pollutants typically associated with AMD pollution in the Witbank, Ermelo and Highveld 
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coalfields. Figure 3.86 shows the spatial distribution classes of rock-AMD reactivity within these 
coalfields as resampled from the geology dataset, using the results of the experiment. 
 
Figure 3.86: Rock-AMD reactivity map of the study area showing the relative classification in 
terms of extraction of AMD pollutants 
3.5 SUMMARY 
Chapter 3 reported the full details of how the SPT approach for the assessment of groundwater 
vulnerability of a typical coalfield with particular reference to AMD pollution and the input datasets 
used for the approach were derived. The approach is based on three broad factors, namely sources, 
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transportation pathways and traps, which were derived from the mineral systems, petroleum and 
source-transport-attenuation approaches. A total of ten parameters, namely rainfall, topography, 
slope, surface and subsurface sources of AMD pollution, soil clay content, rock permeability, 
preferential pathways, aquifer hydraulic conductivity, rock-AMD reactivity and depth to water table 
were used in the approach. 
Other groundwater vulnerability approaches use groundwater recharge as one of the input parameters. 
This parameter is generally a combination of various parameters such as topography, soils and 
rainfall. Using the recharge parameter together with topography, soils and rainfall in the same model 
will result in parameter dependence, where the resultant model would mimic these parameters only 
and mask out the effects of other parameters. In the SPT approach developed in this study, recharge 
information was redistributed to its components and was not used directly in order to minimise 
parameter dependence. Nevertheless, all the necessary parameters affecting groundwater recharge 
were included in the assessment. 
Rainfall was used as a proxy for the availability of water for AMD reactions and as a transport 
medium through which AMD can flow with as it migrates towards the groundwater system. Remote 
sensing was used to extract possible AMD sources on the surface which were combined with the coal 
host rocks to form the AMD sources. The clay content parameter was identified as an appropriate 
parameter with reasonable resolution to address the transport and traps of AMD within the soil layer. 
Laboratory experiment in the research which involves AMD reactions with various soils of varied 
CEC, clay content and types showed that the clay content is a reasonable proxy parameter which 
addresses both the transport of pollution (size of pore spaces) and the number of exchangeable sites 
controlling the traps of AMD as it passes through the soil. 
The possible preferential pathways parameter is very difficult to obtain for an area as extensive as a 
coalfield. Hence, a proxy of the pathways was interpreted from airborne magnetic data which are 
ready available at a reasonable scale covering the entire coalfield area. 
The experiment of neutralising acidity and removal heavy metals from five samples which represent 
the variability of the rock mineralogies found in the study area produced exciting results. The 
dolomite sample was able to extract most of the heavy metal pollutants from the AMD solution and 
was also able to buffer the acidity to a neutral pH. Sandstone was the least effective in terms of 
buffering the acidity and removal of heavy metals from the AMD solution. Sulphate and chloride 
were conservative, as none of the five rock samples was able to significantly reduce the sulphate and 
chloride concentration. Hence, sulphate may be used as a proxy tracer for AMD where its presence 
in the groundwater can be used as an indicator of pollution. 
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CHAPTER 4: KNOWLEDGE-DRIVEN FUZZY EXPERT SYSTEM 
4.1 INTRODUCTION 
In the previous chapter, an approach for the assessment of groundwater vulnerability to AMD 
pollution at a typical coalfield scale was discussed. A total of ten parameters were identified as being 
appropriate for the assessment of groundwater vulnerability to AMD at a regional scale. The next 
significant challenge is to find ways of combining these parameters to generate groundwater 
vulnerability models. There are several approaches, ranging from simple index-weight, knowledge-
driven systems, data-driven systems and hybrid systems. This chapter describes a knowledge-based 
GIS fuzzy expert system which was built to aggregate the ten input map layers using the current 
understanding of AMD pollution migration mechanisms converted into four vulnerability factors 
(sources, transportation pathways and traps) and used to generate a groundwater vulnerability model 
of the coalfields. 
A review of the knowledge-driven system fuzzy expert system will be done, followed by application 
of the system to generate a groundwater vulnerability model of the Witbank, Ermelo and Highveld 
coalfields. The model will be validated, followed by a discussion of the results. 
This chapter is based on Sakala et al. (2018) which was published as part of this research. 
4.2 KNOWLEDGE-DRIVEN ARTIFICIAL INTELLIGENCE SYSTEMS 
The implementation of knowledge-driven AI systems involves an understanding, the design and 
implementation of ways of representing information by means of computers so that programs (agents) 
are able to use this information (Shapiro, 1995): 
• to derive information and relationships amongst inputs; 
• to aid people in natural languages; 
• to support decision taking and future planning; and 
• to solve problems in areas that normally require human expertise. 
4.3 OVERVIEW OF FUZZY EXPERT SYSTEMS 
The fuzzy expert system is centred on the fuzzy logic theory which was developed by Zadeh (1965). 
The theory expresses logic as a continuum of truth or falsehood, as opposed to the classic (crisp) 
tradition where logic is presented as either true or false. The fuzzy expert system is a knowledge-
driven AI technique that involves formulating computer-based systems that are able to extract and 
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copy cognitive reasoning in drawing conclusions. Thus, the computer emulates human thought 
processes (Porwal et al., 2003, 2015). 
The fuzzy expert system may be considered a fuzzy set which consists of fuzzy membership functions 
(FMF) comhi prising fuzzy membership values (FMV). According to Joly et al. (2012), a generalised fuzzy set  is  6giv e(nl  =suc1h I <th >at): if j is7 a set of 7 input layers j  ( = 1 I< 7) with > classes denoted generically by k , then  fuzzy sets hi in j, containing “vulnerable factors” may be 
defined by Equation 4.1 (Joly et al., 2012): 
hi =  m6k, nop q6k  ∈  j 4.1 
Where no is the fuzzy membership function for estimating the fuzzy membership value (weight 
assigned by the hydrogeologist) of 6k in the fuzzy set hi. 
The fuzzy expert system can be implemented to a real application using a three-stage process which 
involves fuzzification, fuzzy engine and defuzzification (Figure 4.1) (Hellmann, 2002). 
 
Figure 4.1: Structure of the fuzzy expert system 
4.3.1 Fuzzification 
In this approach, a fuzzifier converts the crisp input variables into FMV making up a FMF (Figure 
4.1). The FMF as an appropriate function which best describes the relationship of the inputs to the 
output and should be well defined. The fuzzy membership function may be linear, Gaussian or of any 
other type. For the study area, a linear function, given by Equation 4.2 was used (Joly et al., 2012): 
nsit =  H ∗1 u0k00∗ @v   4.2 
where H  is the map weight, uk is the class weight and @v is the confidence factor. 
The map weight H  for each map is subjectively assigned an integer value between 1 and 10 based 
on expert knowledge of the importance of the parameter with respect to groundwater vulnerability 
and whether it is directly or indirectly related to groundwater vulnerability. The confidence factor @v 
of a vulnerability input layer is also subjectively assigned an integer value between 1 and 10 based 
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on the data reusolution and level of uncertainty in the data sources (Porwal et al., 2003). Values of class weights k are assigned values between 1 and 10. Classes with a vulnerability input layer which 
has a high contribution are assigned a high class weight and those with little or no contribution to 
vulnerability are assigned very low class weights approaching zero but never actually reaching zero. 
According to Joly et al. (2012), zero values should not be assigned as they will be transmitted through 
the fuzzy expert system and render the output to be zero even though other layers may show high 
values owing to multiplication with zero in the fuzzy expert system. 
For example, according to Equation 4.2, if a point on the depth to water table map with map weight 
value of 9, a confidence factor of 6 and lying in a class with value of 10 is taken, the fuzzy membership 
value will be given by (9 x 6 x 10)/1 000 = 0.54. 
4.3.2 Fuzzy Inference Engine 
The fuzzy inference engine aggregates the FMF for all the input layers with fuzzy rules to derive the 
fuzzy output (Figure 4.1). The five fuzzy operators (AND, OR, PRODUCT, SUM and GAMMA) 
commonly used for aggregation are discussed in detail by Kanungo et al. (2009) but a summary of 
those used in this thesis will be given in this section. 
4.3.2.1 Fuzzy (AND) operation 
This operator compares the FMVs at each corresponding location on various layer maps and takes 
the minimum values as the output fuzzy value (n) for that particular location. It is appropriate 
where two or more pieces of evidence from layer maps must be present together for a hypothesis to 
be true. The Fuzzy (AND) operator may be expressed by Equation 4.3 (Bonham-Carter, 1994): 
n = ER(n, nw, n , … … … ) 4.3 
Where n is the fuzzy value of map A and nw is the fuzzy value of map B, and so on. 
For example, at some location, when the membership value for map A is 0.5 and for map B, the value 
is 0.25, then the membership for the combination using fuzzy (AND) takes the smallest value of 0.25. 
4.3.2.2 Fuzzy (OR) operation 
This operator compares the FMVs at each corrensponding location on various layer maps and takes the maximum values as the output fuzzy value ( x) for that particular location. It is appropriate for 
any one of the two or more pieces of evidence from the layer maps to be present for a hypothesis to 
be true. The fuzzy (OR) operator may be expressed by Equation 4.4 (Bonham-Carter, 1994): 
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n  x = EPy(n, nw, n , … … … ) 4.4 
Where n is the fuzzy value of map A and nw is the fuzzy value of map B and so on. 
For example, if at some location the membership value for map A is 0.5 and for map B the value is 
0.25, then the membership for the combination using fuzzy (OR) takes the largest value of 0.5. 
4.3.2.3 Fuzzy (SUM) operator 
 This operator combines the F
way that the output result (nMVs at each corresponding location on various layer maps in such a z{) is always larger (or equal to) the largest contributing FMV. 
Therefore, the fuzzy (SUM) behaves as an "increasive" function. This is appropriate where two pieces 
of evidence both favour a hypothesis reinforcing one another and the combined evidence is more 
supportive than either piece of evidence taken individually. The expression for the fuzzy SUM is 
given by Equation 4.5 (Bonham-Carter, 1994): 
nz{ = 1 − |M
 (1 − n) 4.5 
Where n is the fuzzy membership function for the ith map, and i= 1, 2 ... n maps are to be combined. 
For example, where at some location the membership value for map A is 0.5 and for map B the value 
is 0.25, then the membership for the combination using fuzzy (SUM) would be 1-(1-0. 5)×(1-0.25) = 
0.625. 
4.3.2.4 Fuzzy (PRODUCT) operator 
This operator combines the FMVs in such a way that the output result tends to be very small owing 
to the effect of multiplying several numbers <1 (Bonham-Carter, 1994). The output is always smaller 
than, or equal to, the smallest contributing membership value, and is therefore a "decreasive" function. 
This is appropriate where two pieces of evidence contribute to a hypothesis with the result being 
smaller than either pieces of the evidence. The expression for fuzzy (PRODUCT) is given by 
Equation 4.6 (Bonham-Carter, 1994): 
n M}xz = |
 n 4.6 
Where n is the FMF for the i-th map, and i = 1,2,... n maps are to be combined. 
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For example, assuming at some location, the membership value for map A is 0.5 and for map B the 
value is 0.25, then the membership for the combination using fuzzy (PRODUCT) would be 0.5 * 0.25 
= 0.125. 
4.3.2.5 Fuzzy (GAMMA) operator 
This operator may be expressed in terms of the fuzzy (SUM) and fuzzy (PRODUCT) operators by 
Equation 4.7 (Bonham-Carter, 1994): 
n{{ = (nz{)~ ∗ (n}xz)
.~ 4.7 
Where  is a gamma value chosen between 0 and 1. 
The result produced with  = 1 is the same as the fuzzy (SUM) result and result for  = 0 is same as 
for the fuzzy (PRODUCT). Therefore, the fuzzy (GAMMA) operator creates a flexible compromise 
between the "increasive" tendencies of the fuzzy (SUM) and the "decreasive" effects of the fuzzy 
(PRODUCT). The choice of the gamma value should be such that the resultant output (n{{) 
reflects the likely subjective decision making of a typical expert. For example, assuming at some 
location the membership value for map A is 0.5 and for map B the value is 0.25, and  = 0.5 is 
chosen. The resultant output after applying the fuzzy (GAMMA) operator would be given by 
Equation 4.8: 
n{{ = (0.625).‚(0.125)
..‚ = 0.2795 4.8 
4.3.3 Defuzzification  
In this step, a defuzzifier converts the fuzzy output membership values in the crisp output variable 
(Figure 4.1). The crisp output variables express the results of the modelling process, which may be a 
mathematical function or subjectively or objectively defined (Porwal et al., 2003). Several methods 
are available for defuzzification, but the most important criterion to consider when selecting a method 
is that the small change in inputs of a fuzzy model should not cause a significant change in the output 
result (Hellendoorn and Thomas, 1993). In this study, the natural break (ESRI, 2006) was used for 
the defuzzification process. 
4.4 APPLICATION OF THE FUZZY EXPERT SYSTEM TO 
GROUNDWATER VULNERABILITY ASSESSMENT 
The application of knowledge-driven fuzzy expert system approaches to groundwater vulnerability 
assessment is not new and has been successfully used in nitrate pollution studies (Zhou et al., 1999; 
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Dixon, 2005b; Nobre et al., 2007; Pathak and Hiratsuka, 2011). However, the knowledge-driven 
fuzzy expert system has not been used for the assessment of groundwater vulnerability to AMD at a 
regional scale, prompting more research in this area, hence this research was formulated to fill in this 
research gap. Knowledge-based fuzzy expert systems for groundwater vulnerability mapping are 
achieved by extracting the spatial relationships between groundwater vulnerability inputs layers in a 
GIS environment on the basis of the pollution migration, and quantifying and integrating these spatial 
relationships using mathematical logical operators (Dixon, 2005a). Cognitive reasoning is used for 
the formulation of these relationships and the assumptions made are defined. 
4.4.1 Cognitive Reasoning 
In order to apply the fuzzy expert system for assessment purposes, cognitive reasoning for each 
parameter affecting groundwater vulnerability is used in the formulation of fuzzy rules and to assign 
the correct map and class weights. 
4.4.1.1 Sources factor 
4.4.1.1.1 Energy sources 
The cognitive reasoning for the energy source layer is such that groundwater systems under 
topographically flat areas are likely to receive more recharge than those overlain by sloped surfaces. 
The reasoning behind this assertion is that the availability of water in flat areas increases infiltration 
which is responsible for the transportation of AMD reaction products to the groundwater system. The 
effect of evapotranspiration and dilution processes on AMD pollution concentration at a regional 
scale is seldom known, and therefore was not used in this research. 
4.4.1.1.2 Ligand (water) sources 
The availability of water for AMD formation and the transportation of the AMD products also 
contributes to the fate of the groundwater with regards to AMD pollution where water acts as both 
the reactant for the formation of AMD and as a transport medium through which AMD pollution can 
reach the groundwater system. Thus, the likelihood of AMD being formed and transported linked to 
the availability of water constitutes the cognitive reasoning for the ligand sources parameter. 
4.4.1.1.3 Pollutant sources 
The closer the groundwater system is to a potential AMD pollutant source, the higher the likelihood 
of the groundwater system being polluted. This assertion underlies the cognitive reasoning behind the 
pollution sources layer. That is, the further away a groundwater system is from pollutant sources, the 
more the natural attenuation processes filter out the pollutants from reaching the groundwater system. 
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The closer the groundwater system is to potential AMD pollutant sources, the higher the chances of 
the groundwater system being polluted (Ellis et al., 2014). 
4.4.1.2 Transportation pathway factor 
The cognitive reasoning behind the transportation factor assumes that those properties of the soils, 
unsaturated and saturated zones which favour the easy transportation of AMD reaction products also 
contribute to the vulnerability of the groundwater to AMD pollution. That is, soils with a low clay 
content coupled with the presence of preferential vadose pathways, high rock permeability and high 
aquifer hydraulic conductivity tend to facilitate the easy movement of dissolved pollutants, thereby 
increasing groundwater vulnerability. 
4.4.1.3 Traps 
The cognitive reasoning assumptions behind the trap parameter hold that the physical and chemical 
properties (rock-AMD in the unsaturated and saturated conditions, and depth to water table) 
contribute to the natural attenuation of AMD and prevent it from reaching the groundwater system. 
That is, groundwater systems in areas with rocks which lack the ability to extract the AMD pollutant 
coupled with a shallow water table are more vulnerable to pollution owing to their decreased ability 
to attenuate the pollution. 
4.5 FUZZY EXPERT SYSTEM: APPLICATION TO THE WITBANK, 
ERMELO AND HIGHVELD COALFIELDS 
Using the SPT approach developed in this research and cognitive reasoning, a GIS-based fuzzy expert 
system was built and applied to generate a groundwater vulnerability model of the Witbank, Ermelo 
and Highveld coalfield. A three-stage fuzzy expert system involving fuzzification, fuzzy engine and 
defuzzification was used. 
4.5.1 Fuzzification 
Existing knowledge about AMD migration in soils, the vadose zone and aquifers combined with 
cognitive reasoning was used to assign map weights and class weights to various map layers. 
Confidence factors were assigned to an input layer based on the data resolution and level of 
uncertainty, as explained previously. The FMV for each vulnerability layer was estimated from the 
map and class weights and the confidence factor using the linear membership function given by 
Equation 4.2. Table 4.1 shows the map and class weights, the confidence factors and the fuzzy 
membership values for each of the ten crisp layer maps used in this research. In order to visualise the 
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translation of the cognitive reasoning, graphs of fuzzy functions versus crisp variables were plotted 
in Figure 4.2a, b and c to depict the sources, transportation pathway and trap factors respectively. 
Table 4.1: Assigning map weights, class weights and confidence factors for various layers 
 
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Figure 4.2: Crisp to fuzzy translation for (a) sources factor, (b) transportation pathway 
factor, (c) traps 
4.5.1.1 Assigning map weights, class weights and confidence factors for the sources factor 
The ligand (water) source layer was assigned a map weight value of 9, as water is one of the main 
inputs into AMD reactions and is responsible for the transportation of the reaction products. Surface 
sources of the AMD pollution map layer were also assigned a map weight value of 9 because the 
pyritic minerals found in these sources are exposed to atmospheric conditions where all the elements 
needed for the formation of AMD are present. Hence, surface sources are a very important parameter 
as the groundwater vulnerability assessment is specific to AMD pollution and this parameter relates 
126 
 
 
directly to AMD pollution. Subsurface sources of the AMD pollution layer were assigned a map 
weight value lower than that of the surface sources of the AMD sources layer because, even though 
they contain pyritic minerals, these are partially starved of oxygen (a key ingredient in AMD 
generation) and therefore their effect as an AMD source is diminished. The energy factor was 
assigned the lowest map weight of the parameters used as this parameter is not directly related to 
AMD generation but rather indirectly affects the residence time of reactions and the initial migration 
of the products of AMD reactions. 
The ligand (water) source was assigned the lowest confidence factor of 5, as the dataset was extracted 
from countrywide data available at a relatively low resolution of 1 km. The confidence factors for the 
energy and surface sources of pollution are very high as these parameters were extracted from high-
resolution datasets with a spatial resolution of less than 30 m. The subsurface sources of pollution 
were assigned a confidence factor of 6 as the information was extracted from lower-resolution 
geology data mapped at a scale of 1:250 000. 
The classes for ligand (water) sources were calculated using the natural breaks method (ESRI, 2006). 
Class weight values were then assigned to each class according to the cognitive reasoning and a linear 
increasing relationship assumed between ligand (water) sources and groundwater vulnerability. The 
classes for the energy sources were derived from work by Fox et al. (1997) who established that the 
relationship between infiltration rates and slope angle is linear between 0 and 20% and flattens 
afterwards. The class weights for pollutant sources were assigned using the cognitive reasoning that, 
as the distance from the source increases, the effect of the pollution decreases owing to natural 
attenuation by various earth processes. 
4.5.1.2 Assigning map weights, class weights and confidence factors for the transportation 
pathway factor 
The map weight values of transportation pathway are relatively lower that those assigned for the 
sources factor because they only affect the transportation passage for pollution and not the AMD 
generation or attenuation directly. For the four crisp layers which make up the transportation pathway, 
the soil clay content was assigned a relatively higher map weight value of 6 as the clay content 
parameter affects the initial movement of AMD and contributes to the sorption processes which retard 
the AMD pollution from moving further into the subsurface. Preferential pathways, vadose zone 
permeability and aquifer hydraulic conductivity only affect the transport and thus were assigned a 
map weight value of 4. 
The soil clay content and the preferential pathways were assigned confidence factor of 6 as they were 
derived from data mapped at a scale of 1:250 000. Relative rock permeability values and aquifer 
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hydraulic conductivity values were extracted from literature and a relative comparison of the values 
undertaken to generate the map layers. Since the information was derived from literature and no field 
or laboratory work had been done to generate these parameters a lower confidence factor of 4 was 
assigned to these map layers. 
A linear increasing relationship for soil clay content was used for the classes and class weight values. 
The geological contacts, fractures, joints can act as preferential pathways through which pollution 
can migrate and transportation is restricted around these regions. A conservative buffer zone of 30 m 
was assigned around these geological structures. A higher class weight values of 10 was assigned to 
these geological structures and the buffer zone and values of 1 assigned at distances greater than 30 m 
where the preferential pathways were assumed to be negligible. The class and class weight for rock 
permeability and aquifer hydraulic conductivity were assigned according to the cognitive reasoning 
that the higher the permeability and hydraulic conductivity the more easily the pollution will migrate. 
4.5.1.3 Assigning map weights, class weights and confidence factors for the traps factor 
The depth to the water table layer was assigned a map weight value of 7 as this layer is one of the 
main controls of natural attenuation. In this layer, distance directly affects the travel time of the 
pollution, affecting the degradation and/or retardation processes impacting on the flux of the 
pollution. The rock-AMD reactivity map layer was assigned a map weight value of 7 as this parameter 
plays an important role in controlling the chemical retardation of AMD pollution. 
The confidence factor of rock-AMD was assigned a very high value of 9 because laboratory 
simulation experiments were done in this regard, thereby increasing confidence in the usage of this 
parameter. The confidence factor for depth to water table layer was assigned a value of 5, as the data 
had been derived from spatially located boreholes whose depth to water table data had been 
interpolated between the boreholes to generate the map layer. 
The classes and class weight for the rock-AMD reactivity layer were assigned for various rocks 
according to their reactivity with AMD at room temperature, as suggested by the results from the 
laboratory experiment and their mineral compositions. An increasing linear relationship for depth to 
water table was used to assign the class and class weight. 
4.5.2 Fuzzy Inference Engine 
In order to produce a holistic result which accommodates all three critical factors, a multistage fuzzy 
expert system was used (Figure 4.17). First, the ten input maps were grouped according to their 
respective relevant factors according to the SPT approach, as outlined in Chapter 3. 
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4.5.2.1 Sources factor input (S) 
Energy sources: the topographic slope data were converted into fuzzy values as shown in Figure 4.2 
and Table 4.1. Generally, the study area is marked by a high energy source because over 90% of the 
study is flat with slope values below 5% (Figure 4.3). This means that the residence time over which 
AMD reactions occur and the conditions favouring the infiltration of water are higher for most of the 
study area. 
 
Figure 4.3: Sources of energy in fuzzy space 
Ligand (water) sources: the average long-term rainfall was converted into fuzzy values using the 
translation shown in Figure 4.2. The highest ligand sources values were found in the southeastern 
part of the study area (Figure 4.4) along the foot of the Majuba Mountains (Figure 3.22) where the 
prevalence of relief rainfall is possibly attributable to elevation and such amounts of ligand sources 
129 
 
 
are able to drive pollution migration processes more than in the other parts of the study area with low 
to moderate ligand source values. 
 
Figure 4.4: Sources of ligand (water) in fuzzy space 
Pollution sources: the interpretation of Fe-bearing minerals on Landsat 8 and Sentinel 2 remote 
sensing data was converted to fuzzy values using the translation shown in Figure 4.2a. The spatial 
presentation of the translation is shown in Figure 4.5. Blue represents fuzzy values <0.234 
corresponding to pixels (grid cells) located at distances greater than 174 m from the interpreted Fe-
bearing minerals. Red represents the grid cells close to the interpreted Fe-bearing minerals within the 
84 m zone which were translated to fuzzy values >0.558. 
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Figure 4.5: Surface sources of AMD pollution in fuzzy space 
The subsurface sources were converted to fuzzy values with two distinct zones being presented (0 – 
30 m and > 30 m). The red zone (0-30 m) corresponds to fuzzy value 0.240 and the grid cells located 
at distances greater than 30 m correspond to fuzzy value (0.048) and are marked in blue in Figure 4.6. 
Areas with high fuzzy values are located from the centre to the north where coal-bearing rocks (Ecca 
Group) are found and the southern part, without these rocks, is marked by low values. 
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Figure 4.6: Subsurface sources of AMD pollution in fuzzy space 
The fuzzy functions for AMD surface sources and the subsurface (Ecca Group rocks) sources were 
aggregated using a fuzzy (OR) operator to produce the pollutant sources layer (Figure 4.7). The fuzzy 
(OR) operator was used as any one of two sources can act as a source of AMD pollution which can 
affect the groundwater system. The result was divided into four classes (at the source, closer to the 
source, further away and furthest away from the source) using the geometric interval method (ESRI, 
2006) (Figure 4.7). Most of the study area lies within the (further away) class which is represented in 
green in Figure 4.7. The colour blue in Figure 4.7 represents areas where coal seams were not mapped 
and current mining operations fall within the orange to red areas. 
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Figure 4.7: All sources of AMD pollution in fuzzy space constituted by combining surface and 
subsurface sources 
The areas in red (Figure 4.7) mostly denote coal mining waste rock, tailings facilities and loading 
bays. These areas which are rich in pyritic minerals when exposed to oxygen and rain have a higher 
potential to form AMD. If proper waste management of these facilities is not practiced, any leakage 
can trigger the migration of AMD pollution into the subsurface and ultimately the groundwater 
system. 
The three sources (energy, ligands and pollutants) were combined using the fuzzy (SUM) operator to 
produce the sources factor (MFS) in fuzzy values. The fuzzy (SUM) operator was chosen as it takes 
into consideration small changes in each of the input map layers. Thus, the generated source factors 
map is a good reflection of all the input map layers used to generate it. Figure 4.8 shows the resultant 
sources map in fuzzy values. 
133 
 
 
 
Figure 4.8: Sources factor produced by integration energy, ligand (water) and pollution 
sources 
4.5.2.2 Transportation pathway factor input (P) 
Soil clay content: the soil clay content layer was converted to fuzzy values using translation, as shown 
in Figure 4.2. The central part to the eastern end of the Witbank coalfield and the northern edge of 
the Ermelo and Highveld coalfields is marked by high fuzzy values because of high clay content. The 
Highveld coalfield and the southern part of the Ermelo coalfields are marked by relatively low fuzzy 
values owing to soils with a higher clay content there (Figure 4.9). 
134 
 
 
 
Figure 4.9: Transportation pathways in soils (clay content) expressed in fuzzy values 
Preferential pathways: Figure 4.10 shows the preferential pathways which were interpreted from 
geological maps and airborne magnetic data expressed in fuzzy values according to translation, as 
shown in Figure 4.2. These pathways are more prominent in the area between Standerton, Ermelo 
and eMalahleni where an extensive network of Karoo dolerite dykes and sills was mapped. The 
presence of this extensive network of dykes may be an indication of the weakness within the 
subsurface as the emplacement of dykes normally occurs at weak zones of the crust. 
135 
 
 
 
Figure 4.10: Preferential pathways expressed in fuzzy values 
Rock permeability: the rock permeability layer extracted from the literature values was translated into 
relative fuzzy values. The results of the translation are shown in Figure 4.11. The high values are 
found along major rivers with well-developed alluvial systems where the permeability values are 
relatively higher than for most rocks in the study area. Areas where sandstones were mapped are 
marked by relatively higher permeability values than for most rocks but lower than for those of the 
alluvial systems. The other rocks were assigned accordingly with diabase and dolerite ranked at the 
bottom of the list as these are characterised by very low permeability values and thus the lowest fuzzy 
values. 
136 
 
 
 
Figure 4.11: Rock permeability expressed in fuzzy values 
Aquifer hydraulic conductivity: the high fuzzy values are found along rivers with well-developed 
alluvial systems, making up the intergranular aquifer system characterised by high hydraulic 
conductivity values. Conversely, low values are found in areas where shales, mudrocks were mapped 
owing to the low hydraulic conductivity values of these rock formations (Figure 4.12). 
137 
 
 
 
Figure 4.12: Aquifer hydraulic conductivity expressed in fuzzy values 
The transportation pathway factor is made up of soil clay content, preferential pathways, vadose zone 
permeability and aquifer transport (hydraulic conductivity). These parameters with their respective 
fuzzy functions were combined using the fuzzy (SUM) operator to produce the transportation 
pathway factor (MFT). Figure 4.13 shows the resultant transportation pathway factor map depicting 
variations in the AMD transport properties of the study area. Good transport properties were identified 
in the Witbank coalfield and in the eastern part of the Ermelo coalfield as a result primarily of the 
presence of soils with low clay content (<17.6%) coupled with the presence of subsurface rocks with 
138 
 
 
high permeability and hydraulic conductivity. Areas surrounding the major rivers in the Witbank 
coalfield also have good AMD transport properties, making the underlying aquifer vulnerable to 
pollution. 
 
Figure 4.13: Transportation pathways factor generated by combining AMD transport 
parameters in the soil, vadose zone and the aquifer system 
4.5.2.3 Traps factor input (T) 
Rock-AMD reactivity: the results of the laboratory experiments carried out in Chapter 3 on the effects 
of various rocks on the chemical attenuation of AMD were converted into fuzzy values using 
translation, as shown in Figure 4.2. The results displayed in Figure 4.14 show that the biggest portion 
of the study area is marked by high fuzzy values for rock-AMD reactivity. This may be ascribed to 
the sandstones which constitute the majority of the coalfields. These rocks comprise quartz minerals 
which are chemically non-reactive in the AMD environment over a short period of time. In the 
139 
 
 
western part of the study area around Delmas, low fuzzy values are the result of the presence of 
dolomites with high neutralising capacity as discussed in the rock-AMD reactivity experiment in 
Chapter 3 section 3.4.5.10. 
 
Figure 4.14: Rock-AMD reactivity expressed in fuzzy values 
Depth to water table: the depth to water table map layer was converted into fuzzy values using 
translation as shown in Figure 4.2 and Table 4.1. The results are displayed in Figure 4.15. The area 
140 
 
 
in the centre of the study area is marked by a very shallow depth to water table, hence the high fuzzy 
values. 
The rock-AMD reactivity and the depth to water table maps were combined using the fuzzy (SUM) 
operator to produce the traps factor (MFT). The results are displayed in Figure 4.16 which depicts 
high fuzzy values in the central part of the study area characterised by sandstone, granite and alluvium 
with very low acid-neutralising capacity and a shallow depth to the water table. The north-western 
and south-eastern areas are characterised by average to good trapping properties because of the 
presence of rocks with the ability to attenuate AMD chemically and a deeper water table where 
pollution is likely to be attenuated before reaching the groundwater. 
 
Figure 4.15: Depth to water table expressed in fuzzy values 
141 
 
 
 
Figure 4.16: Traps factor generated by combining natural AMD trapping parameters in the 
soil, vadose zone and the aquifer system 
4.5.2.4 Resultant fuzzy output model 
The resultant three factors (sources, transportation pathways and traps) were then aggregated using 
the fuzzy rule given by Equation 4.9. Figure 4.17 illustrates the multistage fuzzy inference network 
which shows the relationship between the various input parameters and the fuzzy operators used for 
fuzzy modelling. The fuzzy (AND) operator was used in the fuzzy rule because all three factors must 
all be true and combine together in making the groundwater vulnerable to pollution. 
(;> (/ 7<"B=><@>I"  (( ))  JJ**<<77((  II<<  EE ) PRG 
;();„>/R= ("
 (B;*) J J**<<77(( I I< E
) PRG 4.9 < E…†)‡  ) 
 
142 
 
 
Where S – source factor, MFS – input FMF for the source factor, P – transportation pathway factor, 
MFT – input FMF for the transportation pathway factor, T – traps factor, MFA – input FMF for the 
traps factor and Vul – groundwater vulnerability, MFvul – output FMF for the groundwater 
vulnerability output. 
 
Figure 4.17: Multistage fuzzy inference network used for combining input layers to produce 
the groundwater vulnerability model 
In this study, the fuzzy (AND) operator was used, as has been done by other authors, to combine 
various layers to produce groundwater vulnerability maps (Dixon, 2005b; Pathak and Hiratsuka, 
2011; Fijani et al., 2013). 
4.5.3 Defuzzification 
Defuzzification, which is a process of translating fuzzy outputs of a function back to crisp variables 
was done in ArcGIS using the natural breaks method (ESRI, 2006). The defuzzification results 
(Figure 4.18) show four groundwater vulnerability crisp variables (high, moderate, low and very low) 
making up the groundwater vulnerability model of the Witbank, Ermelo and Highveld coalfields. The 
study area falls in the main Karoo basin where the hydrogeological conditions warrant the usage of 
the Irish model given by Daly and Warren (1998). The Irish model describes groundwater 
vulnerability in terms of four classes (high, moderate, low and very low). 
The results show that the western, central and the southern areas have moderate to low vulnerability 
owing to a combination of interconnected factors which enhance the natural attenuation and/or 
extraction of AMD pollutants thereby preventing it from reaching the groundwater system. The 
central to eastern part of the Witbank coalfield and the northern part of the Ermelo coalfield are 
marked by moderate to high groundwater vulnerability values. The distribution of classes in terms of 
143 
 
 
aerial coverage is shown in Table 4.2. The distribution of the groundwater vulnerability classes 
follows a skewed normal distribution curve, with the largest population being the moderate class and 
the high class being the smallest in terms of aerial extent (Figure 4.19). 
 
Figure 4.18: Resultant groundwater vulnerability model of the Witbank, Ermelo and 
Highveld coalfields 
144 
 
 
Table 4.2: Aerial coverage of various vulnerability classes 
 
 
Figure 4.19: Aerial size distribution of various groundwater vulnerability classes 
4.5.4 Model Validation of the Fuzzy Expert System 
Groundwater vulnerability results are a relative comparison of various areas in terms of which area 
is more likely to be polluted than the others are. Therefore, there are no universally accepted 
validation procedures, as vulnerability results are relative and vary from place to place. Validation of 
groundwater vulnerability results is often done by a comparison of the results using measurable 
parameters which may be considered as a pollution tracer (e.g. nitrate) (Nobre et al., 2007; Saidi et 
al., 2010; Fijani et al., 2013). 
4.5.4.1 Model validation using hydrochemistry data 
4.5.4.1.1 Correlation coefficient approach 
In the study area, AMD is associated with high sulphate concentrations above the South African 
guidelines (SANS, 2011) for drinking water (Bell et al., 2001). From Chapter 3, it was shown that 
sulphate is relatively conservative and may be considered as a tracer for AMD pollution. Based on 
these findings, sulphate concentration in boreholes from the 2013 sampling programme was used to 
validate the produced groundwater vulnerability model, where it was assumed that the sulphate values 
145 
 
 
in the groundwater are attributable to one or more of the vulnerability factors (energy, pollutant 
sources, transport and traps). 
The spatial variation of sulphate concentrations in groundwater samples within the study area is 
shown in Figure 4.18, where samples with less than 200 mg/L are represented by green triangles and 
those greater than 200 mg/L are represented by a circle with a white star. It is interesting to note that 
groundwater samples with a high sulphate concentration coincide with moderate to high groundwater 
vulnerability zones while samples with low sulphate concentrations lie in low to very low 
groundwater vulnerability zones. 
A correlation analysis between model values and AMD indicators (sulphate) was done and a scatter 
plot produced, as shown in Figure 4.20. Correlation scatter plots between model values and measured 
parameters show high correlation coefficient value (	) values of 0.809 which show a strong positive 
correlation between the fuzzy model and sulphate concentration in the groundwater. 
 
Figure 4.20: Correlation scatter plots for sulphate against groundwater vulnerability model 
values 
4.5.4.1.2 Cross-section method of validation 
To test the validity of the fuzzy groundwater vulnerability assessment using SPT inputs, sulphate data 
from a different source to the one used for the correlation coefficient approach was selected as a 
pollution indicator. Borehole hydrochemistry data from the National Groundwater Archive (NGA) 
with verified locations were tested for ionic balance and only those with an ionic balance of less than 
± 5% were selected for model validation. Sulphate data from 60 boreholes within the study area were 
used to compare relative SO -4  concentration to vulnerability values. The kriging interpolation method 
was used to generate the sulphate concentration map of the study area, as shown in Figure 4.21. The 
map shows high sulphate concentrations in the Olifants catchment covering the area south of 
eMalahleni and Middelburg. To illustrate this validation test, a cross-section, A–B, was created on 
146 
 
 
the vulnerability and the sulphate maps and values extracted to make profiles (Figure 4.22). The 
comparison of these cross-sections enabled an evaluation of the validity of the vulnerability map. 
The comparison between the map of sulphate concentrations and the vulnerability maps shows that 
areas with high sulphate concentrations in the groundwater correspond to the highest vulnerability 
values whereas those with low sulphate concentrations are correlated with the lowest vulnerability 
values. This coincidence is very clear in the northern section of the cross-section between distances 
10 to 140 km. 
 
Figure 4.21: Sulphate concentration map generated from the NGA database 
147 
 
 
 
Figure 4.22: Profile along cross-section A–B showing the DWS borehole sulphate 
concentrations and the fuzzy vulnerability model profile 
The profile (Figure 4.22) differs slightly towards the southern end of the section where the fuzzy 
model values increase slightly although the sulphate concentration remains constant. This could be 
attributable to gridding artefacts as there are no gridding points in this area which is at the edge of the 
gridded areas. 
4.5.4.2 Validation using geophysical techniques 
Geophysical techniques can be used to estimate in situ hydrogeological parameters (porosity, 
permeability, particle size) which, in turn, can be used to validate a groundwater vulnerability model. 
Electrical resistivity tomography (ERT) and seismic refraction techniques were done at four sites (1 
to 4) which fall into very low, low, moderate and high groundwater vulnerability classes respectively. 
The aim of the surveys was to determine whether various modelled groundwater vulnerability classes 
are able to produce measurable geophysical responses which can, in turn, be used as a model 
validation tool. 
4.5.4.2.1 Materials and methods 
Resistivity method 
The concept behind the electrical survey is based on the current flow through a subsurface medium 
consisting of variˆous layers of material with different resistances to current flowing through them where resistivity  of a material is a measure of how well the material resists the flow of electrical current. Resistivity surveys are doneP on the g‰round, where an electrical current ( ) is injected into the ground using a set of electrodes ( ) and ( ) and the earth’s response is measured as a voltage 
148 
 
 
difference (
) at potential electrode (E) and (R), as shown in Figure 4.23. The apparent resistivity 
can be calculated using Equation 4.10 (Loke, 2000): 
ˆ =  
  4.10 
Where 
, the voltage, is the difference of the potential electrodes and  is the current injected by the current electrode.  is the geometric factor which depends on the configuration of the electrodes — 
for example Wenner, Schlumberger, dipole-dipole, pole-dipole and other hybrid configurations. 
 
Figure 4.23: Simple layout of conventional four-electrode array used to measure the 
subsurface resistivity 
The choice of the configuration depends on the purpose of the survey and is controlled by factors 
such as survey costs, available manpower, target feature configuration and geology. In this research, 
the hybrid Wenner-Schlumberger configuration was used as it offers good depth and lateral resolution 
in a sedimentary setting such as that found in the study area. A multi-electrode configuration of the 
Wenner-Schlumberger array with an electrode spacing of 5 m was used. The resistivity values 
obtained from the field survey were inverted to apparent resistivity values using the RES2DINV 
program. The program calculates apparent resistivity and displays them as a pseudo-2D resistivity 
section using the finite difference method with a robust inversion constraint. To produce the pseudo 
2D resistivity section of the subsurface, the program first subdivides the subsurface into a number of 
small blocks and then uses a least-squares inversion scheme to determine the appropriate resistivity 
value for each block. The resistivity values for each block are then combined to produce a 2D pseudo 
resistivity section.  
To convert resistivity values into porosity, Archie’s Law (Archie, 1942) can be used. For the 
sandstone and to cater for both saturated and unsaturated conditions, Archie’s Law was modified by 
Everett (2013) and is given by Equation 4.11: 
Š = /Š‹ ‹MbŒ 4.11 
149 
 
 
where Š is the conductivity of the rock, / is a constant that depends on the pore cementation 
Štort uosity, grain size and shape, fluid wettability and clay content and ranges between 0.4 and 2, ‹ represent the conductivity of water which ranges between 0.3 and 1 where 0.3 represents very 
h iMgh salinity and 1 represents fresh water,  ‹M  is a constant that specifies the level of saturation, i.e. ‹ = 1 for fully saturated conditions. b presents the porosity and H is the cementation exponent which 
depends on grain shape and lies within the range 1.2–2.2 for sandstone. 
Rewriting Equation 4.11, the porosity can be estimated by Equation 4.12: 
b =  /ŠŠ MŽ
/Œ‹ ‹  4.12 
UHs ing values, / = 2, Š‹ = 1,  ‹M  = 1 for saturated conditions and  ‹M  = 0.5 for unsaturated conditions, = 2, resistivity values were converted to porosity as in Equation 4.13: 
b =  2 ∗Š1∗ 1!
 = Š2
!  v<> "/IB>/I @<7I<7" 
b =  2 ∗ 1Š∗ 0.5
! = (Š)
! v<> B7"/IB>/I @<7I<7"
4.13 
 
Seismic refraction method 
The seismic method is a geophysical technique which involves measuring the acoustic impedance of 
the subsurface and deducting the velocities which are related to the density. This is done by hitting 
the surface to generate a seismic signal which travels underground. The generated seismic waves are 
either reflected or refracted upon reaching an interface between two rock layers. The time of arrival 
of the seismic signal is extracted from the seismic trace and used to calculate the velocities and depths 
of different geological boundaries (Geosphere, 2007). The velocity information carries information 
about the nature of the rocks. Important hydrogeological parameters can be deduced from the seismic 
data. In this particular case, seismic information was collected with the overall goal of testing whether 
areas with different groundwater vulnerabilities would produce a measurable velocity contrast and 
for verifying whether these results could be used as a model validation tool. A detailed description of 
the seismic refraction method can be found in any standard geophysics textbook such by as Telford 
et al. (1990). 
In this study, geophones which measure the arrival of the seismic wave were set up at 5 m spacing 
intervals and a hammer was used to produce the seismic waves by hitting a metal plate placed on the 
ground (Figure 4.24). A geode 72 channel seismic system was used for the data acquisition. 
150 
 
 
 
Figure 4.24: Simple layout of conventional seismic refraction survey 
4.5.4.2.2 Results and discussion 
Survey site 1 
A resistivity survey was carried out at survey site 1 along a south–north-oriented 250 m line and the 
measured resistivity values inverted with the results displayed as pseudo 2D resistivity-depth section 
(Figure 4.25a). The resistivity section showed low resistivity values in the top layer probably due to 
wet soils observed on the surface. Figure 4.25b shows the porosity distribution along survey site 1. 
Generally, porosity increases with depth where the estimated porosity for weathered sandstone ranges 
between 9 and 25%. The low porosity values down to 8% are associated with fresh sandstone with 
less porosity owing to compactness and less weathering. High porosity values of the weathered 
sandstone and soils may be an indication of large matrix void spaces which are typically associated 
with weathered rock masses. With reference to groundwater vulnerability this could be a possible 
justification for why this area falls in the high groundwater vulnerability class. 
151 
 
 
 
Figure 4.25: 2D resistivity survey results for site 1 showing (a) the modelled apparent 
resistivity-elevation, (b) the derived porosity-elevation and (c) seismic velocity plot 
Figure 4.25c shows the seismic velocity distribution along survey site 1. Generally, velocity increases 
with depth where the estimated velocity of the soil, weathered sandstone and fresh sandstone are 578, 
2 747 and 3 378 m/s respectively, as shown in Figure 4.25c. Possible faults were also interpreted at 
the site which could act as conduits through which pollution migrates. This complements the 
resistivity results and offers a possible reason why the site is classified as highly vulnerable. 
Survey site 2 
A resistivity survey was carried out along a south–north-oriented 250 m line. The resistivity values 
were inverted with the results displayed as pseudo 2D resistivity-depth section (Figure 4.26a). The 
152 
 
 
resistivity section showed high resistivity values in the saturated zone below the water table 
corresponding to the location where coarse-grained sandstone had been mapped. The survey line 
passed through several ponds, as highlighted in Figure 4.26. This was responsible for the low 
resistivity values recorded near the surface and below the locations of the ponds. 
 
Figure 4.26: 2D resistivity survey results for site 2 showing (a) the modelled apparent 
resistivity-elevation plot, (b) the derived porosity-elevation plot and (c) the seismic 
velocity plot 
The resistivity parameter which is the inverse of conductivity, was converted to porosity, using 
Equation 4.13. The resultant porosity distribution along the survey line at site 2 is shown in Figure 
4.26b. The porosity distribution at site 2 ranges between 1.5 and 14.2%, where the fresh sandstone 
was characterised by very low porosity values. 
The high values corresponded to weathered sandstone and soils. This is in agreement with findings 
by several authors (Tuǧrul, 2004; Navarre-Sitchler et al., 2015) who carried out experiments and 
153 
 
 
found that, as sandstones weathers, the porosity increases owing to the dissolution of cementing 
material surrounding the sandstone matrix, thereby creating openings which increase the porosity. 
Above the water table in the unsaturated zone, the porosity values range from 6.8 to 26.2% slightly 
less than those obtained at survey site 1. Below the water table, the porosity values vary widely, 
ranging between 4.1 and 34.2%. Apart from a possible fault which was interpreted at distance 150 m, 
the resistivity layers were continuous. The inferred fault is also visible on the seismic plot, as shown 
in Figure 4.26c. The seismic plot (Figure 4.26c) shows three layers with average seismic velocities 
295, 2 991 and 3 745 m/s which were interpreted as corresponding to soils, weathered sandstone 
(aquifer) and fresh sandstone respectively.  
The survey site falls in the high to moderate groundwater vulnerability class and the porosity values 
of the weathered sandstone which constitutes the aquifer range between 5 and 14 % with the high 
values below the estimated water table line. 
Survey site 3 
A resistivity survey was carried out at site 3 along a south–north-oriented line of length 250 m with 
the aim of establishing the hydrogeology parameters which can be used to validate the groundwater 
vulnerability model. The resistivity values from field observations were inverted and the results 
displayed as a pseudo 2D resistivity-depth section (Figure 4.27a) for site 3. The resistivity section 
shows an increase in resistivity values with depth, probably reflecting a change in the weathering 
profile of the sandstone. Resistivity values at site 3 range from 15 to 1425 Ohm*m and, although the 
water table line could not be interpreted from this site, according to the regional depth to water table, 
it is located at around 9 m below the ground surface. 
Using equation (4.13), the resistivity parameter, which is an inverse of the conductivity, was 
converted to porosity and the resultant porosity distribution for site 3 is shown in Figure 4.27b. The 
porosity distribution decreases with increasing depth as the degree of weathering decreases. The top 
layer is marked by a high porosity value of over 24% and resistivity values of below 20 Ohm*m could 
be attributed to clay material. A black clay layer was observed in an excavated trench, as shown in 
Figure 4.28. These observations are correlated with the location of the site on the regional clay content 
map (Figure 3.39) where the site falls in the 21–30% clay content region. This layer can act as a 
protective barrier, preventing pollution from reaching the underlying aquifers in the area. 
154 
 
 
 
Figure 4.27: 2D resistivity survey results for site 3 showing (a) the modelled apparent 
resistivity-elevation plot, (b) the derived porosity-elevation plot and (c) the seismic 
velocity plot 
 
Figure 4.28: Black clay layer observed overlying the weathered sandstone at an excavated 
trench next to the surveyed site 3 
155 
 
 
The seismic plot at site 3 (Figure 4.27c), as anticipated, shows an increase in seismic velocity with 
depth as the density of the rocks and the compaction increases. The top low velocity layer was 
interpreted as soil underlain by higher-velocity layers. The seismic velocity of the weathered 
sandstone which forms the aquifer system has an average seismic velocity of 4 505 m/s which is 
slightly higher than that observed at site 2. The fresh sandstone at site 3 is marked by an average 
seismic velocity value of 5 723 m/s. 
A possible fault zone was interpreted at distance 140 m where there is a depression zone visible on 
both the resistivity and seismic velocity plots. This fault zone may act as a possible preferential 
transport zone for pollution from the surface to the aquifer system. 
Considering the location of site 3 in Figure 4.18, it can be seen that this site falls within the moderate 
fuzzy groundwater vulnerability class. Thus, the presence of the protective clay layer, despite the 
interpreted fault zone, may account for why the fuzzy expert system model predicted a moderate 
groundwater vulnerability class. 
Survey site 4 
A resistivity survey was carried out at site 4 along a west–east-oriented line of length 250 m with the 
aim of establishing the hydrogeology parameters which can be used to validate the groundwater 
vulnerability model. The site falls within the groundwater vulnerability low class. The resistivity 
values from field were inverted and the results displayed as a pseudo 2D resistivity-depth section 
(Figure 4.29a) for site 4. The resistivity section shows an increase in resistivity values with depth 
probably reflecting a change in the weathering profile of the sandstone, similar to the observation at 
the other sites. Resistivity values at site 4 range from 16 to 1 681 Ohm*m. Using Equation 4.13, the 
resistivity parameter, which is an inverse of conductivity, was converted to porosity and the resultant 
porosity distribution for site 4 is shown in Figure 4.29b.  
The porosity distribution decreases with depth as the degree of weathering decreases, similar to what 
was observed at site 3. The top layer is marked by a high porosity value of over 19% and resistivity 
values of below 28 Ohm*m which may be accounted for by the clayish material as observed during 
fieldwork. The field observations are correlated with the location of the site on the regional clay 
content map (Figure 3.39) where the site falls in the 30–43% clay content region. Thus, the site is 
marked by higher clay content than that observed at the other surveyed sites. This layer may also act 
as a protective barrier preventing pollution from reaching the underlying aquifers in that area. 
The seismic plot at site 4 (Figure 4.29c), as anticipated, also shows an increase in seismic velocity 
with depth and a fault zone was interpreted at this site. The layers were interpreted on the basis of 
their average seismic velocities where 356, 5 406 and 5 887 m/s correspond to soil, weathered 
156 
 
 
sandstone and fresh sandstone respectively. The seismic velocities of the weathered sandstone, which 
forms the aquifer system, has an average seismic velocity of 5 406 m/s which is slightly higher than 
that observed at all the other sites. This may be attributed to the high degree of compaction of the 
sandstone, as the sandstone found in the Highveld coalfield comprises fine-grained and well-
cemented quartz minerals. 
 
Figure 4.29: 2D resistivity survey results for site 4 showing (a) the modelled apparent 
resistivity-elevation, (b) the derived porosity-elevation and (c) the seismic plots 
The presence of a protective clay layer at site 4 may provide a possible explanation as to why the 
fuzzy expert system model predicted low groundwater vulnerability in this area. 
4.5.4.2.3 Summary 
A comparison of the porosity and seismic velocities at the four sites was done to establish if there is 
any correlation between the measured earth’s properties (geophysical responses) and groundwater 
157 
 
 
vulnerability. Table 4.3 summaries the geophysical responses compared to fuzzy model values for 
each of the surveyed sites. It can be seen that high seismic velocities and low porosities values are 
associated with areas with low fuzzy model values and the opposite is true for low seismic velocities 
and high porosities. Thus, even though only a few sites were surveyed, a relationship between 
geophysical responses (porosity and seismic velocity) and groundwater vulnerability can be drawn 
but if a statistical validation is to be done then a large number of sites need to be surveyed to obtain 
a statistical valid result such as a correlation coefficient value. 
Table 4.3: Comparison of derived porosity values and groundwater vulnerability model 
values for each of the survey sites 
 
4.6 DISCUSSION 
The fuzzy expert system used in this chapter belongs to the knowledge-based branch of AI where the 
parameter weighting factors were subjectively assigned but due diligence was done to ensure that 
most of the information with regard to AMD generation, transport and attenuation processes which 
can be obtained on a regional coalfield scale was used sparingly in the assessment. This may account 
for the strong correlation between the groundwater vulnerability model and the field measurements. 
The strong correlation may be explained as follows: 
• The choice of parameters (S, P and T) and the allocation of appropriate weight allocations 
together with the selection of appropriate fuzzy operators made it possible to model AMD 
migration processes at a regional scale and was key to the production of a groundwater 
vulnerability model which is fairly consistent with field realities (water chemistry – sulphate 
concentration and geophysical responses). 
• The knowledge-based fuzzy expert system used to produce the vulnerability model was able to 
mimic the thought processes of a human. For example, from a human perspective, areas with 
high sulphate concentrations are indicative of AMD and the AI model also shows high 
groundwater vulnerability model values in these areas. 
A comparison of the resultant groundwater vulnerability model with the locations where surface 
AMD pollutants are known to occur shows that some areas marked as highly vulnerable are located 
158 
 
 
at or close to the interpreted AMD sources, with AMD signatures also appearing near monitoring 
boreholes. One possible explanation may be that these areas lack natural pollution attenuation 
properties, with AMD pollution easily travel and reach the groundwater system; hence it can be 
detected by the sampled boreholes. This may also indicate movement of AMD pollution from the 
surface or near-subsurface to the groundwater in these areas. Moreover, the groundwater vulnerability 
model shows low vulnerability in areas such as Delmas even though AMD sources are present. This 
may be attributable to the strong natural attenuation of AMD as the area is located in dolomitic terrain 
which is known to have better AMD buffering capabilities coupled with poor subsurface and soil 
transport properties. This is also evidenced the absence of an AMD signature in the monitoring 
boreholes within these areas. 
The limitation of the methodology is that it does not account for the horizontal travel of pollutants, 
pollution travel time and residence (exposure) time. Where a highly invulnerable area is exposed to 
pollutants over a long period of time, an AMD signature may become evident, whereas a very 
vulnerable area exposed to pollutants for only a short period of time may not show an AMD signature. 
4.7 SUMMARY 
The SPT input vulnerability factors (sources, transportation pathway and traps) were integrated in a 
GIS environment using a knowledge-based fuzzy expert system to rank areas in terms of groundwater 
vulnerability to AMD pollution. Readily available data used to produce the four vulnerability factors 
were sourced from various governmental agencies. The high correlation between groundwater 
vulnerability model values and measured parameters (sulphate) and estimated porosity and seismic 
velocities proves the scientific defensibility of the approach in its use for policy and decision makers 
in the context of land use planning and water management research. Thus, the methodology provides 
a cost-effective approach to evaluating regional-scale areas whose results can provide useful spatial 
information. 
The fuzzy expert approach used to combine the input maps for the SPT approach is based on a 
computer-based system which is solely dependent on the expert’s cognitive reasoning which is 
translated into rules which are aggregated to generate a knowledge-driven groundwater vulnerability 
model. Other AIs which can deduce the relationships between the inputs and measurable parameters 
(known as data-driven approaches) may also be used for combining the SPT inputs and will be 
discussed in Chapter 6 and 7. However, first the pre-requisite data pre-processing and automation 
steps for data-driven approaches are discussed in Chapter 5. 
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CHAPTER 5: DATA PREPARATION AND AUTOMATION FOR 
DATA-DRIVEN ARTIFICIAL INTELLIGENCE 
MODELLING 
5.1 INTRODUCTION 
The previous chapters discussed the preparation of a methodology to assess groundwater vulnerability 
specific to a coalfield setting. A knowledge-driven model was formulated and validated in Chapter 4. 
The other AIs which can be used are data-driven approaches where the relationships between input 
map layers and measureable parameters are used in the development of data-driven groundwater 
vulnerability models. In order to utilise the data-driven algorithms, the input maps need to be tested 
for spatial associations with known polluted sites and binary maps created and pre-processed as 
outlined in this chapter. Some of the work in this chapter was extracted from a peer-reviewed 
publication (Sakala et al., 2017a) written as part of this research. The research was presented at the 
13th International Mine Water Association Congress in Lappeenranta, Finland in 2017. 
5.2 SELECTION OF TRAINING SITES 
In generating the training data, sulphate in groundwater was used to extract proxies for polluted (P) 
and non-polluted (NP) sites. The general assumption is based on the rock-AMD experimental results 
discussed in Chapter 3 where it was established that sulphate was preserved across various geological 
formations and can be used as possible tracer. The conservative value of 200 mg/L of the South 
African guidelines on potable water was used to partition sulphate in the groundwater where values 
lower than 200 mg/L were considered as NP sites and those above 200 mg/L as P sites. Of the 53 
boreholes, 33 have values above 200 mg/L and were assigned a binary value of one (1) while the rest 
below 200 mg/L were assigned value zero (0). 
5.3 MODEL SELECTION 
After representative borehole locations were selected both with and without pollution, the next step 
was to use them for data-driven approaches. Before data-driven approaches are applied, the following 
question needs to be answered first: 
• How is the best model going to be selected? 
• How do we measure the performance of the model? 
To answer these questions in the present study, various techniques were used including the generation 
of algorithms to determine the optimum parameters. These parameters are spatially associated with 
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known polluted groundwater and only the sections of the map layer showing a spatial association 
with high sulphate in groundwater were used. Thus, the following will be discussed in addressing 
these questions, with particular reference to the Witbank, Ermelo and Highveld coalfields: 
• spatial association testing of input map layers; 
• creation of binary map layers; 
• determination of optimum parameters for the generation of the best model; and 
• model input data splitting algorithms.  
5.3.1 Spatial Association Testing of Input Map Layers 
In selecting the parameters to be used for modelling by means of data-driven approaches, a spatial 
association between the available map layers and boreholes with sulphate concentration (> 200 mg/L) 
is made based on the assumption that only that region of the parameter which is spatially associated 
with high sulphate boreholes is somewhat related to AMD pollution in groundwater. The spatial 
association test involves measuring the degree to which elements are similarly arranged in space 
(Carranza, 2002). The distance distribution method by Bonham-Carter (1994) was modified and used 
to identify which section of a map layer is spatially associated with known polluted sites. In the 
method, the cumulative frequency distribution curve for each input layer (rainfall, slope, surface 
sources, subsurface sources, soil clay content, distance to preferential pathways, rock permeability, 
aquifer hydraulic conductivity, depth to water table and AMD-rock reactivity relative values) and 
cumulative frequency at every high sulphate borehole are plotted against the layer values. The graph 
will show the range of map layer values where boreholes with high sulphate concentrations are found. 
Carranza (2002) modified this approach for mineral prospectivity modelling by including calculations 
of theoretical (expected) values which are compared with the cumulative frequency plot for deposit 
locations and a difference curve plot generated. The map layer or map section with positive difference 
values is spatially associated with the location of the deposit. This approach works well for mineral 
exploration data where the predictor map layers are mostly a function of distance from a geological 
feature (fault, contact, shear zone, dyke, etc.) but the approach does not work well for groundwater 
vulnerability datasets such as rainfall or depth to water table. The approach was tested and it was 
realised that a negative spatial association was obtained in the region of the map, while the cumulative 
frequency plot for known polluted sites shows that a large number of boreholes lie within that region. 
Based on this, only the cumulative frequency distribution curve was used to extract the range of values 
of the map layer where over 50% of the polluted sites are found. 
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For every borehole location wI ith layer value 5v with / counts and the total number of boreholes with high sulphate concentration , the frequency  is given by Equation 5.1: 
v = /I 5.1    
For the first layer value, 5
, the frequency v
 is given by Equation 5.2: 
v
 = /I
 5.2    
For the second layer value, 5!, the frequency v‘! is given by Equation 5.3: 
v! = /‘
 I+ / 5.3  ‘!  
And so on, until the last layer value, 5M, where the frequency v  is given by Equation 5.4: 
vM = /(M.
I) + /
M
M 5.4    
The calculations for the cumulative frequency for each borehole with high sulphate values were done 
for all the maps and graphs drawn for each. The relationships between the parameters used for the 
calculations are shown in Table 5.1. 
Table 5.1: Relationships of parameters used for the calculation of spatial association 
 
5.3.1.1 Ligand water sources (rainfall) layer 
Figure 5.1 shows the cumulative frequency plot results of the rainfall map layer. The plot shows that 
from the lowest rainfall value to 662 mm no boreholes with high sulphate were found. Between 662 
and 714 mm the number of boreholes with high sulphate values increased to just over 80% at 714 mm 
and reached 100% at 776 mm. Based on the spatial location of boreholes with high sulphate 
concentrations when compared to rainfall data, the range 662 to 714 mm is the region where most of 
the boreholes are located which may mean that this amount of rainfall may be correlated with the 
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availability of water for AMD reactions and also drives the AMD pollution from the surface to the 
groundwater. The classification into two binary classes (1 and 0), as shown in Figure 5.2 was based 
on a spatial association test carried out on the rainfall map. The map shows that the central part of the 
study area falls within the binary class (1) where all the boreholes with sulphate concentrations 
>200 mg/L are found. Other boreholes with low sulphate concentrations also fall within the areas 
classified as class (1) possibly because rainfall is not a direct parameter which determines sulphate 
concentration in the groundwater. Hence, other parameters are also considered in the following 
sections. 
 
Figure 5.1: Spatial association test results for the rainfall parameter 
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Figure 5.2: Rainfall map layer in binary format 
5.3.1.2 Energy sources (slope) layer 
The cumulative frequency plot for the slope parameter shows that 100% of boreholes with high 
sulphate concentrations are found in the slope range 1 to 5% (Figure 5.3). Thus, according to these 
results, sulphate in the groundwater may be associated with flat areas where infiltration is higher than 
runoff, giving enough time for AMD to infiltrate together with the water into the subsurface. This is 
in agreement with the general assumption made in the current research and the infiltration-slope 
relationship by Fox et al. (1997) that states that areas with flat surfaces favour vertical infiltration of 
water more than runoff. A cut-off value of 5% was used to generate the binary map of the study area 
(Figure 5.4). 
164 
 
 
 
Figure 5.3: Spatial association test results for the slope parameter 
 
Figure 5.4: Slope map layer in binary format 
5.3.1.3 Surface sources of AMD layer 
Figure 5.5 shows the cumulative frequency plot for the surface sources of the AMD pollution layer. 
The plot increases sharply from 0 to 80% within the range 0 to 871 m up to 97% after which the 
gradient flattens at 100% at a distance of 2 384 m. The results clearly show that between 0 to 871 m 
away from the remote sensing interpreted AMD sources, over 80% of the boreholes with high 
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sulphate values are located within this region. The possible explanation is that the closer the 
groundwater system is to surface sources within the 871 m horizontal distance, the higher the 
possibility of AMD entering the groundwater system. Thus, proximity to the mapped sources may 
playing an important role in making the groundwater vulnerable to AMD as can be deduced from this 
plot. Hence the distance 0 to 871 m was assigned a binary class value (1) and those areas further away 
than 871 m were assigned a binary value (0), as shown in Figure 5.6. The areas assigned a value (1) 
are found near the major towns and the Witbank coalfield has the largest area with interpreted AMD 
surface sources. 
 
Figure 5.5: Spatial association test results for surface sources parameter 
5.3.1.4 Subsurface sources of AMD layer 
The plot of cumulative frequency for subsurface sources is almost a straight line from 0 to 100% 
within a very short distance from the location of the subsurface sources (Figure 5.7). This shows that 
almost all the boreholes with high sulphate values are located within or very close (within 248 m) to 
the subsurface sources. Thus, the high sulphate in boreholes is found within a distance of 248 m from 
the coal host rocks. 
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Figure 5.6: Surface sources map layer in binary format 
 
Figure 5.7: Spatial association test results for the subsurface sources parameter 
The spatial association test results of the subsurface sources show that those boreholes with high 
sulphate concentrations are located within 248 m of the coal-hosting geological formations. Hence, 
the distance 0– 248 m was assigned a binary class value (1) and those areas found further away than 
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248 m assigned binary value (0), as shown in Figure 5.8. The areas assigned a value (1) are found in 
the northern parts of the Ermelo and Highveld coalfields and over almost the entire Witbank coalfield. 
 
Figure 5.8: Subsurface sources map layer in binary format 
5.3.1.5 Soil clay content layer 
The cumulative frequency plot for soil clay content shows an increase in the frequency of boreholes 
with high sulphate concentrations from 0 to 91% within the 12 to 25% clay content zone (Figure 5.9). 
This may mean that boreholes with high sulphate concentrations are found in areas with less soil clay 
content which is in agreement with the general assumption used for formulating the fuzzy expert 
system. Areas with between 12 and 25% soil clay content are spatially associated with high sulphate 
in the groundwater while areas with a soil clay content above 25% are not. Hence, a binary class value 
(1) was assigned to areas with 12 to 25% soil clay content, as shown in Figure 5.10. Almost the entire 
Witbank coalfield and the area between Carolina and Ermelo are characterised by a low clay content, 
as represented in red in Figure 5.10. 
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Figure 5.9: Spatial association test results for the soil clay parameter 
 
Figure 5.10: Soil clay map layer in binary format  
5.3.1.6 Preferential pathway layer 
Figure 5.11 shows the cumulative frequency plot for the pathways layer. The plot shows three breaks 
(305 m, 892 m and 3 851 m) where the gradient changes and the percentage of boreholes change from 
50% to 84% to 100%. The extent to which a mapped pathway can contribute to groundwater 
vulnerability as a possible pathway for pollution is highly localised around the structure. Thus, 
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considering the breaks, the 305 m region surrounding the structure was selected as a zone in respect 
of which the preferential pathway can be effective and slightly over 50% of the boreholes are located 
in this zone. Thus, proximity to the geological features which could indicate possible zones of 
weakness within the subsurface plays an important role in determining the vulnerability of 
groundwater to AMD. Hence, the distance 0–305 m was assigned a binary class value (1) and those 
areas found further away than 305 m were assigned a binary value (0), as shown in Figure 5.12. 
 
Figure 5.11: Spatial association test results for the pathway parameter 
 
Figure 5.12: Pathway map layer in binary format 
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5.3.1.7 Aquifer hydraulic conductivity layer 
The spatial association test for the aquifer hydraulic conductivity layer shows that below 4 no 
boreholes with high sulphate concentrations were found. The cumulative frequency plot (Figure 5.13) 
shows 0% cumulative frequency from relative hydraulic conductivity (2 to 4). From relative hydraulic 
conductivity values 4 to 6, the number of boreholes with high sulphate values increased to 100% at 6 
which flattened out afterwards with no change in the number of borehole beyond this value. Thus, 
the range of values (4–6) is where all the boreholes with high sulphate were found. Figure 5.14 shows 
that a large section of the map falls in the binary class (1). 
 
Figure 5.13: Spatial association test results for the relative aquifer hydraulic conductivity 
 
Figure 5.14: Relative aquifer hydraulic conductivity map layer in binary format 
171 
 
 
5.3.1.8 Rock permeability layer 
The spatial association results for rock permeability show a straight line between 1 and 7 where fewer 
than 4% of boreholes were found. Within the 7– 8 range of rock permeability values, the frequency 
of boreholes with high sulphate increased from 4 to 100% and flattened afterwards (Figure 5.15). The 
7 – 8 range is the region characterised by relative permeability values with the largest numbers of 
boreholes with high sulphate concentrations. Thus, the results show that rocks with relatively higher 
permeability values are spatially associated with locations of boreholes with high sulphate 
concentrations. The high rock permeability association with high sulphate in the groundwater may be 
an indication of the link between the increased interconnectivity of pores in the rocks with movement 
of AMD pollution through the rocks up to the groundwater system.  
The spatial association results were used to produce the binary map (Figure 5.16) where binary value 
(1) was assigned to areas with rock permeability values between 7 and 8 and other areas with 
permeability values outside this range were assigned a value (0). Binary class (1) assigned to rocks 
with relative permeability values between 7 and 8 covers the central to eastern part of the Witbank 
coalfield and the area between Ermelo and Carolina. These areas correspond to areas with sandstone, 
rhyolite, basalts, gabbro and felsite rock types. These rocks have high permeability values indicating 
the ease with which water and pollution can flow. 
 
Figure 5.15: Spatial association test results for the relative rock permeability parameter 
172 
 
 
 
Figure 5.16: Relative rock permeability map layer in binary format 
5.3.1.9 Rock-AMD reactivity layer 
Figure 5.17 shows the cumulative frequency plot for the contribution of rock-AMD reactivity towards 
groundwater vulnerability. The contribution of rock-AMD reactivity is an inverse of the relative rock-
AMD reactivity values given in Table 3.9. It must be noted that from relative values 1 to 9, fewer 
than 4% of the boreholes with high sulphate concentrations are found. The frequency increases 
sharply to 100% from relative values 9 to 10. Thus, areas with rocks which lack the capacity to extract 
the pollutants from AMD have high relative contribution to making the groundwater vulnerable to 
AMD; hence most of the boreholes with high sulphate are found in these areas, as seen by the high 
frequency of boreholes at high relative values. Rocks such as sandstone, alluvium and diamictite are 
found in this range of values. Figure 5.18 shows the spatial distribution of the binary classes (1 and 
0) for the Witbank, Ermelo and Highveld coalfields. The contribution of rock-AMD reactivity values 
9 and 10 which correspond to alluvial, sandstone and shales were assigned a binary class value (1) 
because of their spatial association with high sulphate in the groundwater. The other relative rock-
AMD reactivity classes were assigned a binary class value (0) as they showed no association with 
high sulphate concentrations in the groundwater. 
173 
 
 
 
Figure 5.17: Spatial association test results for the rock-AMD reactivity parameter 
 
Figure 5.18: Rock-AMD reactivity map layer in binary format 
5.3.1.10 Depth to water table layer 
The depth to water table in the study area ranges between 4.8 and 21.8 m. The spatial association plot 
for depth to water table is a sigmoid shape with the frequency of boreholes increasing linearly from 
4.8 to 12 m after which the gradient decreases from 12 m and flattens at 100% at depth values greater 
than 13.9 m (Figure 5.19). Thus, from 4.8 to 12 m, over 89% of the boreholes with high sulphate 
174 
 
 
concentrations are found in this region. Areas with depth to water table values of between 4.8 to 12 m 
were assigned a class value (1) and those with values above 12 m assigned a binary class value (0) 
(Figure 5.20). 
 
Figure 5.19: Spatial association test results for the depth to water table parameter 
 
Figure 5.20: Depth to water table map layer in binary format 
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From the depth to water table graph (Figure 5.19) it can be said that the groundwater systems with 
water table values below 12 m from ground surface are potentially vulnerable to AMD pollution as 
seen by the large frequency of boreholes with high sulphate concentrations in this range of values. 
Table 5.2 summarises the binary class allocations for all the map layers using the spatial locations of 
boreholes with high sulphate concentrations. 
Table 5.2: Assignment of binary classes 
 
Given that the input map layers of the SPT approach needed to be reclassified into binary format 
using cumulative frequency graphs, a selection of zones within each map where over 50% of the 
boreholes are located was completed. The next task was the selection of data-driven approaches for 
combining the ten maps into one map. Various approaches exist but in this research only two machine 
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learning AI systems were used namely the Artificial Neural Networks (ANN) and the Adaptive 
Neuro-Fuzzy Inference System (ANFIS). But before these approaches could be applied, it was 
necessary to formulate algorithms to determine the general optimal parameters. In the following 
sections algorithms are discussed which were used to automate some of the processes for using AI to 
generate groundwater vulnerability models. 
5.3.2 Determination of Optimal Data-Driven Model Parameters 
In the design of data-driven approaches for rapid groundwater vulnerability assessments, the 
determination of optimal parameters is required to enhance the performance of the AI system. The 
parameters to be determined include the number of training iterations, termed “epochs”, for all 
machine learning (data-driven); these include both the ANN and the ANFIS approaches and a number 
of neurons in the hidden layer of the ANN approach. A full description of ANN and ANFIS are given 
in Chapter 6 and Chapter 7 respectively. 
5.3.2.1 Epoch determination algorithm for data-driven approaches 
Binary map data are feed into a data-driven AI algorithm where training is carried out at various 
training iterations (epochs) with a fixed initial number of neurons in the hidden layer for training. The 
initial number of neurons in the hidden layer may be determined randomly or by using calculations 
by Shigidi and Garcia (2005).The trained model at each epoch is used to classify/predict test datasets 
(with known output values) which had not been used in the training. The training epoch (M) with the 
least error between the predicted and the known value is selected as the optimum number of epochs. 
The step by step procedure for the epoch determination algorithm is given in Appendix 3.1. 
5.3.2.2 Hidden layer neurons determination algorithm for data-driven approaches 
Using the optimum number of epochs (M) as fixed, the machine learning algorithm is run with 
varying numbers of neurons in the hidden layer. For each neuron in hidden layer training step, the 
learnt system is used to determine the output values of a validation dataset. The predicted value is 
compared with the actual values and the error is returned for each training point. The number of 
neurons in the hidden layer with the least error between the predicted values and the actual is the 
optimum number of neurons in the hidden layer (H). The procedure for this algorithm is found in 
Appendix 3.2. 
5.3.2.3 Data splitting algorithms 
Using the optimum number of neurons in the hidden layer (H) and epochs (M) the next task is to 
determine the best data split for the data-driven algorithm modelling. This can be done using a data 
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splitting algorithm (holdout, random, k-fold and leave-one-out). Choice depends on the data size, 
randomness, speed, etc. By considering the nature of the dataset used for groundwater vulnerability 
assessment and the comparison of the various data splitting algorithms, the k-fold and the leave-one-
out will be used in this research.  
In summary, the leave-one-out algorithm splits the data into three datasets: training, validation and 
testing. During training, the algorithm excludes one point from training and uses it for validation 
before repeating the same process with the next point until all the points have been used as validation. 
The algorithm works best for small datasets and is very slow for bigger datasets. Details of the leave-
one-out algorithm can be found in Appendix 3.3. 
The other data-splitting algorithm is the k-fold cross-validation approach, which involves splitting 
the data into folds (partitions). During training, the algorithm excludes one fold from training and 
uses it for validation before repeating the same process with the next fold until all the folds have been 
used as validation. The algorithm works best for larger datasets and cannot be used for small datasets 
where splitting into folds is not possible. Details of the leave-one-out algorithm can be found in 
Appendix 3.3. A special case of the k-fold, called the stratified k-fold, will be used. The stratified k-
fold ensures that each generated fold contains ones and zeros in almost the same representation as the 
original dataset before splitting (Kohavi, 1995). The advantages of using the stratified k-fold cross-
validation is that the original dataset structure is preserved. Thus, the model produced is validated 
using datasets with a similar structure, resulting in a more representative validated model than the 
model generated without the stratification. This is particularly important when the generated models 
are intended for critical application such as informing policy and decision makers (as is the focus of 
this research). 
5.4 DISCUSSION 
Determination of the region of a map layer which is spatially associated with high sulphate in 
groundwater is particularly important as this will highlight only the region of the map layer which is 
associated with AMD pollution, given the assumption that high sulphate in groundwater can be used 
as a proxy of polluted sites. 
Conversion of map layers to binary form reduces the dimensions of the data but is necessary in view 
of computer memory constraints. Binary maps are used for data-driven modelling as this will reduce 
the number of permutations for the ten map layers to accommodate the current limits of the virtual 
memory of a personal computer. This is done because if the full data spectrum datasets were to be 
used, an excessively large number of permutations would be generated which cannot be processed by 
a personal computer at this time. 
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In the development of rapid groundwater vulnerability assessment tools, using data-driven 
approaches, the stratified tenfold and leave-one-out cross-validation approaches are selected owing 
their advantages over other techniques such as the random subsampling and holdout techniques. For 
a large dataset, the stratified tenfold approach is preferred and for a small dataset the leave-one-out 
method is used. An algorithm which verifies the size of the dataset and decides which of these two 
approaches to used needs to be designed and incorporated into the assessment tools. This inter-link 
between algorithms will ensure that the results are generated fast and very accurately. 
5.5 SUMMARY 
The spatial association test was thus successful in extracting only those sections of the input map 
layers and map layers which are spatially associated with high sulphate in groundwater. Next, the 
results are used to generate binary maps for each selected parameter. Algorithms to be used to 
automate some of the processes for data-driven approaches such as establishing the number of epochs 
and number of neurons in the hidden layer and the selection of the best model are also given. A 
detailed explanation of artificial neural networks and the neuro-fuzzy system will be presented in 
Chapters 6 and 7. 
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CHAPTER 6: DATA-DRIVEN ARTIFICIAL NEURAL NETWORK 
SYSTEMS 
6.1 INTRODUCTION 
The SPT approach was developed and successfully used to generate a knowledge-driven groundwater 
vulnerability model for the Witbank, Ermelo and Highveld coalfields. Another approach that can be 
used to generate groundwater vulnerability models is a data-driven approach where the system learns 
from given known input-output data pairs and where it deduces meaningful relationships which can 
be used to determine output values when only input values are given. 
In the Chapter 5, data preparation techniques and algorithms for the automation of some processes 
were discussed. In this chapter, a data-driven artificial neural network system will be formulated and 
used to generate a groundwater vulnerability model for the Witbank, Ermelo and Highveld coalfields. 
The generated model will also be validated and discussed. 
6.2 OVERVIEW OF DATA-DRIVEN ARTIFICIAL NEURAL 
NETWORK SYSTEM 
6.2.1 Biological Neural Network Background 
Artificial neural networks are inspired by the biological nervous system, also known as the natural 
neural network or biological neural network. Therefore, it is of paramount importance to understand 
the basic functioning of biological neural networks. Most highly developed animals and humans who 
have the ability to adapt to a changing environment are equipped with a complex control system 
which is capable of learning. This is facilitated by a very complex network of highly specialised 
neurons ~ 1011 of them making up the building blocks of the central nervous system (Schmidt, 2000). 
A neuron contains all the structures of an animal cell and can be broken down into three main 
components, namely the soma (cell body for information processing), the dendrite (for receiving 
information) and axon (for sending information). Dendrites form a tree-like network of nerve fibres 
which are connected to the soma (Seyam, 2009) (Figure 6.1). The soma is the spherical compact area 
of the neuron that contains the nucleus and fluid material called the cytoplasm surrounding the 
nucleus. The axon is a long slender projection of the neuron that typically conducts electrical impulses 
away from the soma of the neuron. Axons are connected to one another by synapses. The transmission 
of signals from one neuron to another at synapses is a complex chemical process in which specific 
transmitter substances are released from the sending cell. The effect is to raise or lower the electrical 
potential inside the body of the receiving cell. If the potential reaches a threshold, a pulse is sent down 
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the axon and the cell is ‘fired’ (Ajith, 2005). Together, the neurons form a complex system, with the 
brain as the control unit which operates as a highly sophisticated computer capable of processing vast 
amounts of information at relatively fast speeds and with great precision. 
 
Figure 6.1: Simplified illustration of a biological neuron 
6.2.2 Artificial Neural Network Background  
Artificial neural networks (ANNs) belong to the data-driven branch of AI which is inspired by the 
biological neural system in terms of which the computer is trained to do the functions which, at the 
moment, are best handled by humans, such as learning (Shigidi and Garcia, 2005). Artificial neural 
networks (ANN) form a class of non-linear parallel distributed information processing and adaptive 
systems originally based on studies of the brains of living species (McCulloch and Pitts, 1943). 
The basic building blocks of artificial neural networks are artificial neurons which function similarly 
to their biological counterparts. These building blocks may be regarded as constituting a simple 
mathematical model or function on which complex networks are based. Such a model is made up of 
three simple sets of rules: multiplication, summation and activation (Figure 6.2) (Krenker et al., 
2011).  Initially, inputs are weighted, meaning that every input value y is multiplied by an individual weight . The weights represent the strengths of the interconnections between individual neurons 
inside the neural network and are used to solve a problem. In the centre of an artificial neuron is the 
sum function (j’) that sums all the weighted inputs and bias J, according to Equation 6.1. At the 
exit of an artificial neuron, the sum of previously weighted inputs and the bias are passed through the 
activation function, also known as a transfer function (Figure 6.2). 
j =  Œ’ 
 y ∗  + J 6.1 
where j’ is the weighted sum of inputs which constitute the input to the activation function, 
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 y is the input value in discrete time, “,“ where  goes from 1 to H, and,  is the weight value in discrete time  where  goes from 1 to H, J is the bias. 
 
Figure 6.2: Working principle of an artificial neuron 
In case the weighted sum from the weighted inputs is zero, a bias is added to make the output not-
zero or to scale up the system response. The output from the summation function can be any numerical 
value from -infinity to +infinity. Thus, in order to limit the output response, a threshold value is set 
up. This is done by passing the output response (j’) through the activation function (v). The 
activation function is set as the transfer function used to obtain the desired output. Equation 6.2 
represents the mathematical representation of the relationship between the activation function, inputs, 
weights and the bias: 
6(“) =  v ”Œ
 y(“) ∗ (“) + J• 6.2 
where  y(“) is input value in discrete time “ where  goes from 1 to H, 
 J (“) is the weight value in discrete time “ where  goes from 1 to H,  v is the bias,  6 (i“s )the transfer function,  is the output value in discrete time “.  
182 
 
 
The activation functions which are commonly used are binary, sigmoid or hyperbolic tangent 
(Xenonstack., 2017). The binary function has only two possible output values (0 and 1) (Figure 6.3a). 
This means if the input value meets a specific threshold, the output value (1) is produced and if the 
specific threshold is not met, the output value (0) is produced. This can be described mathematically 
by Equation 6.3.  
6 =  –01  vv  jj’’  O<IIℎℎ>>""ℎℎ<<**  6.3 
The most commonly used activation function in most neural networks is the sigmoid function, which 
manifests as an “S” shaped curve (Figure 6.3b). The sigmoid resembles a Boolean model, as it is 
“off” until a given weighted sum of inputs (WSI) value is reached, then it quickly (but not instantly) 
switches to “on”. This is similar to the step function but is continuous and used simply to calculate 
its derivative. This models the behaviour of a natural neuron, which is generally either “firing” or 
“inactive” (Dan., 2017). The sigmoid function may be expressed by Equation 6.4 which normalises 
the output to values in the range between 0 and 1: 
6 =  1 +  1.˜™š›œ  6.4 
where 6 is the output value after the activation function operation, 
 Š is the steepness parameter that controls the steepness of the curve, 
j’ is the weighted sum of the inputs (Equation 6.1) which feeds into the activation function.  
The hyperbolic tangent function may also be used as an activation function. This function normalises 
the output to values in the range between -1 to 1 (Figure 6.3c) and it may be described by 
Equation 6.5:  
6 =  I/7ℎ ”Œ
 y ∗  + J• 6.5 
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Figure 6.3: Activation functions commonly used in artificial neural networks: (a) binary (b) 
sigmoid and (c) hyperbolic tangent 
For all these activation functions, if the input is lower than the weighted sum of inputs (WSI) the 
neuron is inactive, but as the input increases beyond the WSI, this causes the neuron to “fire”. Altering 
the weights connecting neurons can change the relationships between the neurons, thus changing the 
behaviour of the network. 
Artificial neurons are interconnected in an artificial neural network, where their working principles 
and simple set of rules are combined to solve various complex problems such as automated speech 
recognition, visual recognition, medical diagnosis and signature verification. Artificial neural 
networks have been found to have a sound theoretical basis from the perspective of machine learning 
and usually perform well when used for real-world data analysis (Bishop, 1995). In addition, ANNs 
have good generalisation capabilities and are usually robust against noisy or missing data (Idowu et 
al., 2012). They include the ability to learn and generalise from examples to produce meaningful 
solutions to problems even when the input data contain errors or are incomplete, and to adapt solutions 
over time to compensate for changing circumstances and to process information rapidly (Jain et al., 
2004).  
6.2.3 History of ANNs  
The first information about artificial neural networks was recorded in 1943 when Warren McCulloch 
and Walter Pitts developed the first model of neural networks based on simple elements which were 
considered to be binary devices with fixed thresholds in what was called the “all-or-none” character 
of nervous activity (McCulloch and Pitts, 1943). 
In 1944, Joseph Erlanger and Herbert Spencer Gasser identified several varieties of nerve fibre and 
established the relationship between action potential velocity and fibre diameter. 
In 1949, Hebb introduced in his book “The organisation of behaviour” the concept that neural 
pathways are strengthened each time they are used. This principle is fundamental to the way humans 
learn (Hebb, 1949). 
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In 1958, Rosenblatt introduced the concept of a simple layer network called the perceptrons 
(Rosenblatt, 1958). Another system which used a different learning rule as the perceptron was 
developed in 1960. The system employed the least-mean-squares as a learning rule, expounded in the 
book “Perceptrons: An introduction to computational geometry” by Minsky and Papert (1969). In 
this book, the limitations of single layer perceptrons were demonstrated. The perceptron was defined 
as a two-layer machine that can handle only linear separable problems and cannot solve the exclusive 
“OR” problem. These limitations sent the field into hibernation for the next couple of years. 
In 1972, Klopf developed a basis for learning in artificial neurons based on biological principles 
(Klopf, 1972). 
In 1974, Paul Werbos developed the back propagation learning method. 
Between 1980 and 1986, several events led to the rebirth of the field and several scientists, 
mathematicians and technologists joined the emerging field. In 1982, Hopefield presented a paper 
“Neural networks and physical systems with emergent collective computational abilities” which 
introduced the notion of the recurrent artificial neural network. 
In 1986, the back propagation algorithm was rediscovered by Rumelhart and others, as described in 
the book “Learning internal representation by error propagation” (Rumelhart et al., 1986). Since the 
conception of the back propagation algorithm, papers, books, workshops and conferences dealing 
with ANN have proliferated. 
In 1987, the self-organising neural pattern recognition machine was developed by Carpenter and 
Grosberg (Carpenter and Grossberg, 1987). 
Between the 2009 and 2012, the recurrent neural network and deep feedforward neural networks were 
developed in the research group of Schmidhuber (Schmidhuber, 2014). 
6.2.4 Architecture of ANNs 
Biological neural networks are made up of neurons which comprise connected cells which transmit 
electrical impulses. The electrical activity of a neuron is dependent on the electrical activity of the 
neurons to which it is connected. In the case of artificial neural networks, real numbers are used 
instead of electrical activity. Neurons output a value, which is passed to other neurons via synaptic 
connections and (together with values from any number of other neurons) determines the output of 
those neurons. Synaptic connections are one-way, so values generally propagate through the network 
in one direction. 
Input data from outside the network are fed into the input layer neurons which are connected to other 
neurons in the network via synapses. Neurons in the network are generally arranged in layers or 
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groups of neurons which are linked only to similar groups to their left and right — the input neurons 
(the yellow “blobs” in Figure 6.4) form the first of such layers. Data from the input layer are fed from 
left to right through various hidden layers (the green “blobs” in Figure 6.4). The last layer of neurons 
in the network is known as the output layer (the blue “blobs” in Figure 6.4); the output values of 
neurons in the output layer are the outputs of the network. This layered architecture is inspired directly 
by the design of the brain, in which layers of neuron cells are arranged in an onion-skin pattern (Dan, 
2017). 
 
Figure 6.4: Artificial neural network architecture defined by the way in which neurons 
(yellow, green and blue blobs) are connected by synapses (lines) 
In summary, there are various types of neurons in a neural network where each one generates its own 
output based on its function in the network. The functions of the various neurons may be summarised 
as follows (Dan, 2017): 
• Input neurons: the function of the input neurons is to accept the input and output signal from 
the hidden layer neurons. The output data from the input neuron are the same as those that have 
been accepted from outside the network. 
• Hidden (sigmoid) neurons: the function of the hidden neurons is to perform calculations on the 
data it has received from the input neurons. The output from the hidden neuron is the sum of its 
inputs multiplied by an activation function. The output data are then transmitted to the output 
neuron. 
• Output neurons: output neurons provide a place from which network output values can be read 
from the network from the outside. 
In the past, the ANN was thought to be akin to a “black box” system into which inputs are fed and 
results produced without any explanation of how the inputs are related to one another and how they 
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are combined generate the output. But with our current understanding of how they work from 
fundamental principles we can now obtain the weights relating each input to the output. 
6.2.5 Learning by ANNs 
The main property of a neural network is the ability to learn from its environment, and to improve its 
performance through a learning (training) process. During training, data are fed into the input layer 
which communicates with one or more “hidden layers” where the actual processing is done via a 
system of adjusting the weights “connections”. The ANNs contain some form of “learning algorithm” 
which modifies the weights of the connections according to the input patterns with which it is 
presented (Shigidi and Garcia, 2005). In a sense, ANNs learn by example, in the same way a child 
learns to recognise dogs from examples of dogs. 
Learning by neural networks may be viewed as a case whereby network weights are updated by 
neurons in view of producing the desired output, based on a set of examples. The most common types 
of network training are supervised, unsupervised or hybrid. 
6.2.5.1 Supervised training  
The networks are trained to extract the general relationships between the input layers and given 
outputs from a set of given examples and to store these relationships. After this, the trained ANN is 
given a set of input layers from which it produces an output based on the stored relationships. 
The network learns by adjusting the weight values to reduce the differences between the example 
output (desired) and the training output (actual) until the error is below a certain acceptable value. 
The most commonly used supervised learning algorithm is the back propagation algorithm which 
means that learning is done by backward propagation of the error generated when the training output 
value is compared with the example output.  
6.2.5.2 Unsupervised training 
In this learning category, the network is only supplied with inputs from which it explores the 
underlying structure in the input data, or correlations between patterns in the input data, and organises 
the patterns into clusters. Thus, the neural network adjusts its own weights so that similar inputs result 
in similar outputs. After learning, when the network is given a new set of inputs it will be able to 
predict to which cluster the data belong using patterns and correlations learnt from the previous 
training data input. No external assistance or teacher is required for this category of learning. The 
Kohonen algorithm belongs into this category. 
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6.2.5.3 Hybrid training 
This type of training combines supervised and unsupervised training. Parts of the weights are 
determined through supervised learning and the others are obtained through unsupervised learning. 
6.2.6 Learning Algorithms – Back Propagation using a Sigmoid Activation 
Function 
The back propagation algorithm considers the minimum of the error function in weight space using 
the method of gradient descent. The combination of weights which minimise the error function is 
considered to be a solution for the learning problem. The back propagation algorithm can best be 
categorised into four steps (Rojas, 2005): 
• feed forward computation; 
• back propagation to the output layer; 
• back propagation to the hidden layer; and 
• weight updates. 
The algorithm is stopped when the value of the error function is sufficiently small. 
6.2.6.1 Feed-forward computation 
This step involves computing the output value by summing the weighted inputs and applying the 
activation function for each of the neuron connections in a forward direction. That is, calculations are 
done from the input layer neurons to the output layer neurons via the hidden layer neurons. This is 
achieved by multiplying the initial weight by the input values for each input layer neuron–hidden 
layer neuron connection. All the weighted inputs arriving at each hidden layer neuron are summed. 
The activation function is applied to the summed value to compute the output value for each hidden 
layer neuron. The results from an activation function operation at each of the hidden layer neurons 
become the input values to the output layer neurons. At the output layer neuron, the results from the 
hidden layer neuron activation function are multiplied by the initial weight of each hidden layer 
neuron–output layer neuron connection. Then all the weighted results arriving at the output layer 
neuron are summed and the activation function to generate the output value of the network is applied. 
6.2.6.2 Back propagation to the output layer 
The ouItp>u/t 7value calculated from the previous step (I>/7†ž†) is compared with the actual output value ( Ÿ ¡‘) for that given input value to compute the training error value. The training error 
is back propagated and used to adjust the weight such that the error is minimised. The equation for 
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calculating the error is the derivative of the activation function multiplied by the difference between 
the training output and the actual target value, given by Equation 6.6: 
>><>¢_ = >¤/I¤ ∗ (I>/7Ÿ ¡‘− I>/7†ž†) 6.6 
The sigmoid function for Š =1 is given by Equation 6.7: 
6 (5) =  1 +1 .¥ 6.7 
The derivative of the sigmoid function can be expressed in terms of its original function, as shown 
by Equation 6.8: 
6 5  6(5) =  (1 + .¥.¥)! = 6(5) ∗ (1 − 6(5)) 6.8 
Applying to the sigmoid function, the error is given by Equation 6.9: 
>><>¢_ =  I>/7†ž† ∗ m1 −  I>/7†ž†p ∗ (I>/7Ÿ ¡‘ − I>/7†ž†) 6.9 
After the error has been calculated, it is first propagated from the output layer neurons to the hidden 
layer neurons. The hidden layer neuron-output layer neuron co¦nnections are first adjusted. The expression for adjusting the weight incorporates the learning rate ( ) and the momentum (§). 
The expression is given by Equation 6.10: 
∆‡‘Ÿ M(¢_)= ¦ ∗ >><> ∗ ‡©(¢_) 6.10 
where ∆
¦‡‘Ÿ M(¢_)
 is the delta change in learning for the hidden layer-output layer connection, 
 is the learning rate, 
 >><> is the error calculated using Equation 6.9, and, 
 ‡©(¢_) is the old weight for the hidden layer neuron-output layer neuron connection. 
The new weight will be then be given by Equation 6.11:  
M‘‹(¢_) = ‡©(¢_) + ∆‡‘Ÿ M(¢_) + § ∗ ∆(I − 1) 6.11 
where ∆(I − 1) is the previous delta change of the weight. This is zero for the first iteration. 
 M‘‹(¢_) is the new weight for the hidden layer neuron–output layer neuron connection, 
 ‡©(¢_) is the initial or previous iteration weight, 
189 
 
 §   is the momentum. 
The new weights for all the hidden layer neuron–output layer neuron connections are calculated and 
stored for the next step. 
6.2.6.3 Back propagation to the hidden layer 
In this step, the error is propagated back to the input layer and the weights are adjusted accordingly. 
This is slightly more complicated than propagating the error from the output to the hidden layer that 
was calculated in the previous step using the known target output values. Here, the actual target values 
of the hidden layer neurons are unknown. To solve this problem, we use the new weights and error 
from the previous step. The new weight is multiplied by the error for the hidden layer neuron–output 
layer neuron connections. The equation for this calculation is given by Equation 6.12:  
)‘    = M‘‹(¢_) ∗ >><>¢_ 6.12 
Once the error for the hidden layer nodes is known, weights between the input and hidden layer can 
be updated. First, the rate of change needs to be calculated for every weight, using Equation 6.13: 
∆‡‘Ÿ M( _¢)= ¦ ∗ )‘    ∗ yMž† 6.13 
Then the new weights between input and hidden layer are calculated using Equation 6.14:  
M‘‹(_¢) = ‡©(.¢) + ∆‡‘Ÿ M(_¢) + § ∗ ∆(I − 1) 6.14 
It is important not to update the weights until all the errors have been calculated. Using the new 
weights, the output error is calculated and the results compared with the previous error. This is done 
so as to evaluate the training as the training progresses. In the process, the error decreases until it is 
negligible. At this point, the network is termed to have been “trained” and will be ready for use to 
solve the problem it has been set. 
6.2.7 Types of Artificial Neural Networks  
6.2.7.1 Feed-forward ANNs  
Artificial neural networks with a feed-forward topology are called feed-forward artificial neural 
networks and, as such, have only one condition namely that information must flow from input to 
output in only one direction with no back-loops. There are no limitations on the number of layers or 
type of transfer function used in the individual artificial neurons or the number of connections 
between the individual artificial neurons. 
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6.2.7.2 Recurrent ANNs  
Artificial neural networks with a recurrent topology are called recurrent artificial neural networks. 
These are similar to feed-forward neural networks with no limitations regarding back-loops. In these 
cases, information is no longer transmitted only forwards but can also be fed backwards. This creates 
an internal state which allows the network to exhibit dynamic temporal behaviour.  
The most basic topology of a recurrent artificial neural network is the fully recurrent artificial network 
where every basic building block (artificial neuron) is directly connected to every other basic building 
block in all directions. Recurrent artificial neural networks such as those by Hopefield, Elman, Jordan, 
and bi-directional networks are special cases of this type of neural network. 
The aim of the technique is to train the network such that its response to a given set of inputs is as 
close as possible to a desired output. A number of algorithms are available for training neural 
networks. Back propagation is the most popular training algorithm (Werbos, 1990) and was used in 
this study. During feed-forward artificial neural network training, each hidden and output neuron 
processes inputs by multiplying each input by its weights. The products are summed and processed 
using an activation function. Here, a sigmoid function produces an output with reasonable 
discriminating power. 
6.3 DATA-DRIVEN ARTIFICIAL NEURAL NETWORK: 
APPLICATION TO THE WITBANK, ERMELO AND HIGHVELD 
COALFIELDS 
The application of artificial neural networks for the generation of a groundwater vulnerability model 
is a built up from the conference publication (Sakala et al., 2016) where an ANN was built and used 
for assessment of groundwater vulnerability to AMD at a coalfield. In this publication, the training 
input parameters were DRIST parameters (Depth to water level, recharge, impact of the vadose zone, 
soils and topography) and hydrochemistry data (sulphates and total dissolved solids (TDS)) were used 
as the training output dataset. The SPT approach developed is an extended version of this 
methodology where other parameters such as recharge were replaced with rainfall to factor in the 
water availability for reactions while also capturing the role played by rainfall in the transportation 
of pollutants. 
Using the input parameters as proposed by the SPT approach and an appropriately designed ANN 
system, a groundwater vulnerability model was generated for the Witbank, Ermelo and Highveld 
coalfields. An in-depth description and discussion of the formulation and validation of the model are 
given in this section. 
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6.3.1 ANN Training 
The process followed in the preparation of the ANN groundwater vulnerability model comprises of 
six stages; some of the stages have been discussed in the Chapter 5. The stages involve: 
1. Selection of training polluted and non-polluted sites, where local, national or international 
guideline threshold values for groundwater quality can be used (as discussed in Chapter 5, 
section 5.2); 
2. Creation of the binary input maps based on spatial association test results for each of the input 
map layers (discussed in Chapter 5 section 5.3.1); 
3. Establishing the optimum number of iterations (epochs) and number of neurons in the hidden 
layer which minimise over-fitting. This stage has already been discussed in Chapter 5, but 
results from ANN modelling will be given; 
4. Selection of the cross-validation method involving an algorithm that checks the number of 
training points and decides on whether to use tenfold or leave-one-out cross-validation training; 
5. Using the optimum number of epochs and number of neurons in the hidden layer obtained in 
stage 3 and the appropriate cross-validation training technique (stage 4), the ANN modelling 
algorithm is run to train the ANN network, after which it is then used to predict groundwater 
vulnerability values for all the grid cells within the entire study area; and 
6. The final stage involves reclassifying the predicted ANN output into four groundwater 
vulnerability classes after which the model is validated with data that were not used to train the 
ANN. 
6.3.1.1 Selection of training sites 
As discussed in section 5.2, 53 boreholes within the Witbank, Ermelo and Highveld coalfields which 
were sampled and subjected to hydro-chemical analyses were reclassified into binary (0) and (1) 
values. Those with a sulphate concentration below 200 mg/L (non-polluted sites) were assigned 
binary class (0) and those above (polluted sites) this value were assigned class value (1). 
6.3.1.2 Binary map creation 
Binary maps generated in section 5.3.1 would be used as input map layers and borehole points 
(polluted and non-polluted), also in binary format, would be used as training outputs. 
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6.3.1.3 Establishing the optimum number of epochs and neurons in the hidden layer 
In order to establish the optimum number of epochs in order to obviate the overfitting and inadequate 
training problems which are generally associated with ANN modelling, the epoch determination 
algorithm was used. Overfitting occurs when training the ANN network such that the predicted values 
precisely match the training data instead of producing generalised results as expected from a trained 
ANN. Inadequate training occurs when training is terminated before the network has gathered enough 
information about the relationship between the inputs and output pairs. The inputs to the ANN are 
the ten map layers and borehole sulphate concentrations in the groundwater as training outputs. When 
the epoch algorithm is run, the graph of testing the MSE against the epoch number is displayed. The 
results show that a number of training epochs produce low validation MSE values was obtained using 
8 770 epochs with a validation MSE value of 0.0505 (Figure 6.5). This value was returned and passed 
on to the next algorithm which determined the optimum number of neurons in the hidden layer. 
Details of this algorithm can be found in Appendix 3.1. 
 
Figure 6.5: Validation errors at various training epochs 
The hidden layer neuron number determination algorithm uses the optimum number of epochs to run 
several ANNs with varying number of neurons in the hidden layer and records the overall validation 
MSE for each neuron number. The output MSE values are plotted against the neurons in the hidden 
layer, as shown in Figure 6.6. The optimum number of neurons in the hidden layer with the least 
validation error was found to be nine layers with the lowest validation MSE value of 0.0525. Details 
of this algorithm can be found in Appendix 3.2. 
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Figure 6.6: Validation errors at various number of neurons in hidden layer 
6.3.1.4 Selection of cross-validation method 
A simple algorithm was designed to verify the number of training data points and to choose between 
running the tenfold stratified or leave-one-out cross-validation method. The algorithm works as follows: given  number of training points, the decision to select a particular option is based on the 
structure (o=f) these two options. F(7or= t)he tenfold stratified method to work, the number of points for the polluted  and non-polluted  sites should be greater than ten for each, thus there should be a 
minimum of twenty points with at least ten points being polluted sites and ten points being non-
polluted sites. When the leave-one-out method is used for a large number of training points, the 
computation time is greatly increased. Therefore, for large data points greater than twenty, the 
tenfold-stratified method is fastest as the number of training events is lower. At the same time, for 
fewer points below twenty or for data points which are fewer than ten for polluted and non-polluted 
points the leave-one-out approach is better. This can be summarised with the following expressions: 
v  Q 20 /7 = Q 10 /7 7= Q 10, then use the tenfold stratified method otherwise 
v  < 20 and / or = < 10 and / or 7= < 10 then use the leave-one-out method. 
For the Witbank, Ermelo and Highveld coalfields with 53 boreholes of which 33 are polluted sites, 
the tenfold stratified method was selected. 
6.3.1.5 Artificial neural network modelling 
With the optimum number of training epochs and neurons in the hidden layer and the cross-validation 
method selected, the ANN algorithm is run. For the Witbank, Ermelo and Highveld coalfield study 
area, the topology (input-hidden-output) of the ANN model used was a (10-9-1) model, where 10 is 
the number of input map layers, 9 the optimum number of neurons in the hidden layer and finally 1 
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the number of outputs (sulphate concentration). Figure 6.7 shows the architectural layout of the ANN 
for the ten input map layers. The input layer is connected to the hidden layer by synapses with weights 
which are modified during the training process. The groundwater vulnerability model is the output 
layer. 
The tenfold stratified cross-validation algorithm was run using the optimum values of epochs and 
neurons in the hidden layer which had been determined in the previous stages as 8 770 and 9 
respectively. The results for validation for each training fold (experiment) are presented as a scatter 
plot of error values against the training fold value number (Figure 6.8). Thus, according to the results 
of the training, the lowest validation error is training fold number 4 with a validation error value of 
0.001. This trained fold is therefore returned as the best-trained network for use in predicting 
groundwater vulnerability values for all the other map cell locations (pixel with a resolution of 30 x 
30 m) within the Witbank, Ermelo and Highveld coalfields area. 
 
Figure 6.7: ANN architecture used for training 
195 
 
 
 
Figure 6.8: Graph for determining the best fold with the lowest validation error 
6.3.2 Data-Driven ANN Model Results 
The groundwater vulnerability model values were reclassified into four classes using the natural break 
method (ESRI., 2006) and the results presented in Figure 6.9. The model shows the groundwater 
vulnerability model generated using sulphate training where the areas in blue indicate the lowest 
vulnerability and the red coloured areas show the most vulnerable. The groundwater vulnerability 
model of the Witbank, Ermelo and Highveld coalfields produced using ANN systems shows that the 
largest portion of the area falls in the low groundwater vulnerability class. 
The ANN model shows high groundwater vulnerability values in the area between Delmas, 
eMalahleni and Middelburg. The area to the south of Carolina towards Ermelo is also marked by 
relatively high values. The groundwater vulnerability model is derived from the relationship that the 
network established between the various map layers and the sulphate concentration. Thus, of the ten 
inputs maps, the highest values appear to fall in areas which are characterised by flat surfaces with 
moderate rainfall, close to AMD sources where the soil clay content is low, in the presence of rocks 
with high permeability values and very low rock-AMD reactivity. 
The areas with low groundwater vulnerability may be attributed to a combination of earth properties 
which work together to inhibit AMD from to reaching the groundwater system. These properties 
include a lack of sources of AMD combined with soils and rocks which offer some resistance to the 
flow of pollution and good trapping properties. 
Table 6.1 shows the aerial coverage sizes of the four groundwater classes where the low vulnerability 
class has the largest size and the size distribution decreases as the vulnerability class changes from 
low to high with the high class covering the smallest aerial extent. 
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Figure 6.9: Groundwater vulnerability model of the Witbank, Ermelo and Highveld coalfields 
generated by using ANNs 
Table 6.1: Aerial coverage of various vulnerability classes 
 
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Figure 6.10: Aerial size distribution of various groundwater vulnerability classes 
6.3.3 Validation of the ANN Model 
Before the ANN groundwater vulnerability model can be used for critical applications such as policy 
and decision making in this research, the model needs to be validated by other datasets which were 
not used to generate the model. Three validation methods, namely correlation coefficient, cross-
section and geophysical methods were used. 
6.3.3.1 Model validation using hydrochemistry data 
6.3.3.1.1 Correlation coefficient approach 
The correlation coefficient method for model validation involves a comparison of the model values 
with a parameter which can be measured physically. Some of the boreholes with measured sulphate 
concentrations which were not used for model building were selected for validation purposes. The 
artificial neural network model values at each of these borehole locations were extracted. Sulphate 
was considered to be conservative in Chapter 3 and hence can be used as possible tracer for AMD 
pollution. The spatial locations of six points used for the validation of the ANN groundwater 
vulnerability model are shown in Figure 6.9 as yellow circles with a black dot in the centre. The 
sulphate concentrations in the groundwater at these points were used to validate the model. The 
groundwater samples with a high sulphate concentration coincide with moderate to high groundwater 
vulnerability zones, while samples with low sulphate concentrations lie in low to very low 
groundwater vulnerability zones. A few boreholes were used for validation so that most of the 
boreholes are used for model creation. 
A correlation analysis between model values and AMD indicators (sulphate) was done and scatter 
plots produced as shown in Figure 6.11, where very a high correlation value of 0.909 was obtained 
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showing that the ANN was well trained and was able to predict with high accuracy the model values 
which it had not used for training. When generating the binary map layers, a range of map layer values 
was selected to cover between 50 and 100% of points instead of selecting the region of the map which 
completely covers 100% of the points. This was done so that the ANN can learn the general 
relationship between the various input layers and the spatial locations of the training points so that 
when new points are given to it after learning, it would be able to predict the output values better, as 
was borne out by the present scenario. 
 
Figure 6.11: Correlation scatter plots for sulphate against groundwater vulnerability model 
values 
6.3.3.1.2 Cross-section method of validation 
In order to test the validity of the ANN groundwater vulnerability assessment using SPT inputs, 
sulphate data from a different source was selected as a pollution indicator. Borehole hydrochemistry 
data from the National Groundwater Archive (NGA) with verified locations was tested for ionic 
balance. Only those with an ionic balance of less than ± 5% were selected for the validation of the 
ANN model. The sulphate data from 60 boreholes within the study area were used to validate the 
ANN model by comparing the sulphate with vulnerability values. Again, the kriging interpolation 
method was used to generate a sulphate concentration map of the study area, as shown in Figure 4.21. 
To illustrate this validation test, a cross-section line A–B was created on the ANN vulnerability and 
the sulphate maps. A comparison of these cross-sections enabled an evaluation of the validity of the 
vulnerability map. 
The comparison between the map of sulphate concentrations and the vulnerability maps shows that 
areas with high sulphate concentrations in the groundwater correspond to the highest vulnerability 
values. This coincidence is very clear in the northern section of the cross-section between distances 
10 and 70 km (Figure 6.12). The graphs differ at the start of the section owing to a scarcity of 
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boreholes in this area when compared to the higher resolution of the ANN model. At the northern 
edge of the cross-section, the ANN model values increase yet the sulphate concentration drops. A 
close examination of the sulphate contour map shows that only one borehole with a low sulphate 
value is found in the area, and at the edge, thus the low interpolated values at the edge could be 
attributable to a gridding artefact which normally affects the edges of the gridded data. 
  
Figure 6.12: Profile along cross-section A–B showing the DWS borehole sulphate 
concentration and the ANN vulnerability model profile 
6.3.3.2 Validation using geophysical techniques 
Geophysical techniques (ERT and seismic refraction) were used to estimate in situ hydrogeological 
parameters (porosity and seismic velocity) which were used to validate the ANN groundwater 
vulnerability model. The survey results for the four survey sites are described in Chapter 4, section 
4.5.4.2. The modified Archie’s Law by Everett (2013) was used to convert the inverted apparent 
resistivity values to estimated porosity values. 
From the comparison of the porosity ranges for the unsaturated zone of the four sites and their 
corresponding model values it can be seen that where the porosity values are high, the model values 
are high as well, with low model values being correlated with low porosity values (Table 6.2). 
According to these observations at the four sites, the higher the porosity, the higher the groundwater 
vulnerability values. A comparison of the porosity and seismic velocities at the four sites was done 
to establish whether there is any correlation between the measured earth properties and groundwater 
vulnerability. Table 6.2 summarises the geophysical results in comparison with the ANN model 
values for each site. The four sites surveyed fall in two classes, where the ANN model show values 
1 and 0 for sites (1, 2) and (3, 4) respectively. Only four sites were surveyed to obtain geophysical 
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parameters and the sites with high porosity and low seismic velocities correspond to where the model 
predicts high groundwater vulnerability and where porosity is low and, for high seismic velocity, the 
model values are high. Thus, the model values are correlated with the physically measurable earth 
properties. 
Table 6.2: Comparison of derived porosity values and the ANN groundwater vulnerability 
model values for each of the survey sites 
 
6.4 DISCUSSION 
Automation of some of the stages (i.e. determination of the termination number of iterations and 
number of neurons in the hidden layer) in the application of artificial intelligence for the generation 
of groundwater vulnerability model proves to be quite helpful in terms of processing speed as it 
obviates the trial and error approach which is normally used for these tasks. Automation gives the 
user of the developed tools for assessing groundwater vulnerability to AMD at a coalfield enough 
time to focus on preparing quality input map layers and interpreting the results as opposed to spending 
too much time on processing and modelling the data. 
The ANN tool for the rapid assessment of groundwater vulnerability developed in the current research 
is very dynamic in the sense that upon modification of input training data, when more data of higher 
resolution becomes available, the model is modified accordingly. This is facilitated by the automatic 
algorithms developed during the current research. Owing to the automation of some of the processing 
in ANN modelling, the developed tool will produce results which are consistent even if used by 
different experts to run the modelling using the same input data. This proves to be particularly 
important when results are meant for critical decision making purposes such as mining regulatory and 
land use planning where results may need to be reproduced in the future. 
6.5 SUMMARY 
The ANN tool which belongs to the data-driven branch of AI was generated and applied in the 
creation of the groundwater vulnerability model for the Witbank, Ermelo and Highveld coalfields. 
The tenfold stratified cross-validation technique produced a groundwater vulnerability model which 
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is quiet consistent with field realities based on the validation methods used: correlation coefficient, 
cross-section and geophysics techniques (resistivity and seismics) methods. 
Based on the ANN groundwater vulnerability model of the Witbank, Ermelo and Highveld coalfields, 
the Witbank coalfield has the largest area of highly vulnerable groundwater and the Highveld 
coalfield is the least vulnerable of three coalfields studied. These findings are also reflected by the 
number of mining activities both historic and current found in these coalfields, with most of the coal 
mining operations being concentrated in the Witbank coalfield. The SPT approach is a specific 
groundwater vulnerability assessment technique where sources of pollution are incorporated in the 
modelling; hence, areas where no AMD pollution has been mapped might appear to be of low 
vulnerability. Hence, the model needs to be updated over time as more mining takes place and new 
data are acquired. 
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CHAPTER 7: HYBRID ARTIFICIAL INTELLIGENCE SYSTEM 
7.1 INTRODUCTION 
The previous chapters presented the application of the fuzzy expert and neural network system to 
produce groundwater vulnerability models of the Witbank, Ermelo and Highveld coalfields of South 
Africa. In this chapter, the fuzzy expert system and the neural networks are combined to form a hybrid 
system which combines the benefits of these two powerful systems. An overview and theoretical 
background of the hybrid system will be given, after which a hybrid system model will be developed 
and validated for an assessment of the groundwater vulnerability of the Witbank, Ermelo and 
Highveld coalfields. 
7.2 OVERVIEW OF THE HYBRID SYSTEM 
Hybrid systems combining fuzzy logic, neural networks, genetic algorithms, and expert systems are 
proving their effectiveness in tackling a wide variety of real-world problems. Every intelligent 
technique has particular computational properties (e.g. ability to learn, explanation of decisions) that 
make it suited to particular problems and not to others. For example, while neural networks are good 
at recognising patterns, they are not useful for explaining how they reach these decisions. Fuzzy 
expert systems, which can reason using imprecise information, are good at explaining their decisions 
but they cannot automatically acquire the rules they use to make those decisions. These limitations 
have been a central driving force behind the creation of intelligent hybrid systems where two or more 
techniques are combined so as to overcome the limitations of individual techniques. While the fuzzy 
expert system provides an inference mechanism under cognitive uncertainty, computational neural 
networks offer exciting advantages, such as learning, adaptation, fault tolerance, parallelism and 
generalisation (Porwal et al., 2003). To enable a system to deal with cognitive uncertainties in a 
manner approximating that used by humans, one may incorporate the concept of a fuzzy expert 
system into the neural networks. 
7.2.1 Types of Neuro-Fuzzy Systems 
There are several ways to combine neural networks and fuzzy expert systems. Efforts at merging 
these two technologies may be characterised by considering three main categories: neural-fuzzy 
systems, fuzzy-neural networks and fuzzy-neural hybrid systems (Fuller, 2000). 
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7.2.1.1 Neural-fuzzy systems 
Neural-fuzzy systems are characterised by the use of neural networks to provide fuzzy systems with 
an automatic tuning method, but without altering their functionality. One example of this approach 
would be to use neural networks to formulate membership functions and to map relationships between 
fuzzy sets that are utilised as fuzzy rules (Fuller, 2000), as shown in Figure 7.1. In the training process, 
a neural network adjusts its weights in order to minimise the MSE between the output of the network 
and the desired output (Azar, 2010). 
 
Figure 7.1: Neural-fuzzy system 
The weights of the neural network represent the parameters of the fuzzification function, fuzzy 
membership function, fuzzy rule and defuzzification function. In this sense, the training of this neural 
network results in automatically adjusting the parameters of the fuzzy system and finding the optimal 
values. This kind of combination is mostly used in control systems applications in process automation 
in engineering (Azar, 2010). 
7.2.1.2 Fuzzy-neural systems 
In the fuzzy-neural system, the elements of the neural networks are fuzzified using fuzzy expert 
system theorems. Figure 7.2 shows the general flow diagram of a typical fuzzy-neural system. Crisp 
statements are fed into a fuzzy inference system whose outputs become inputs to an ANN which 
produces the output using a specified learning algorithm. In this case, a crisp neuron may be regarded 
as a fuzzy neuron. The inputs to the fuzzy neurons are crisp, but the weights are replaced by the fuzzy 
membership functions (Lin and Lee, 1996; Azar, 2010). The result of each weighting operation is the 
membership value of the corresponding input in the fuzzy set. Also, the aggregation operation used 
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in fuzzy operators (AND, OR, SUM etc.) can be used in the hybrid system. Since fuzzy neural 
networks are inherently neural networks, fuzzy-neural systems are mostly used in pattern recognition 
applications (Azar, 2010). 
 
Figure 7.2: Fuzzy neural system 
7.2.1.3 Hybrid neuro-fuzzy systems 
In the hybrid neuro-fuzzy approach, both fuzzy and neural networks techniques are used 
independently, where each one serves a different function in the system. Each system incorporates 
and complements each other in order to achieve a common goal. This can be achieved by interpreting 
the fuzzy rule-base in terms of a neural network. The approach is versatile and has a wider range of 
uses than the fuzzy or the neural network systems when these are used individually. That is, the fuzzy 
sets can be interpreted as weights and the rules, and input variables and output variables can be 
represented as neurons. The learning algorithm, similar to that in neural networks, entails a change 
of the weights and/or creating or deleting connections. These changes may be interpreted both in 
terms of a neural net and in terms of a fuzzy controller, thus it is possible to avoid the “black box” 
behaviour of neural nets in this way. 
Hybrid neuro-fuzzy come in various forms, for example, the ARIC (Berenji, 1992), the GARIC 
(Bersini et al., 1993), the ANFIS (Jang, 1993) or the NNDFR model (Takagi and Hayashi, 1991). 
The Adaptive Neural-Fuzzy Inference System (ANFIS) is the most successfully used in combining 
the benefits of two powerful systems (neural network and fuzzy expert system) into a single capsule 
algorithm and will be used in this research. 
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The ANFIS applies neural learning rules to identify and adjust the parameters and structure of a fuzzy 
inference system. This approach has all the benefits of the two systems, including the following (Jang, 
1993; Azar, 2010): 
• easy implementation; 
• fast processing; 
• accurate learning; 
• strong generalisation abilities, excellent explanation facilitated through fuzzy rules; and 
• easy to incorporate both linguistic and numeric knowledge for problem solving. 
The structure and parameter identification of the fuzzy rule base is done by the neural network by 
defining, adapting and optimising the topology and the parameters of the corresponding whole system 
based only on the available data. Thus, the ANFIS may be regarded as both as an adaptive fuzzy 
inference system with the capability of learning fuzzy rules from data and as a connectionist 
architecture provided with linguistic meaning. Fundamentally, ANFIS functions like a fuzzy 
inference system and the Sugeno Tsukamoto fuzzy model is commonly used.  
7.2.1.3.1 ANFIS system operation 
The ANFIS system is made up of five layers (1 to 5): 
Layer 1 is the input module where the system obtains data from the outside world and generates 
output fuzzy values according to the fuzzy membership functions as suggested by the expert. 
Layer 2 is the rule module which takes the output fuzzy values from layer 1 and applies the fuzzy 
rules to combine the inputs using the fuzzy rules as suggested by the expert. 
Layer 3 is the average module. The output from the rule module is normalised according to the firing 
strength of the rules in layer 2. 
Layer 4 is the consequent module which uses the normalised output from layer 3 as inputs to a 
machine learning algorithm. The machine learning algorithm adjust the weights of the nodes using 
the relationship it generates between the normalised outputs from layer 3 and the given output data. 
Layer 5 is the output module which sums up all the incoming signals from layer 4 and generates one 
output value. 
This process is done repeatedly until the system has been trained. 
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To illu
and 6, strate the learning algorithm and for the purpose of simplicity, a network with two inputs, 5  and one output, z, is considered. The first-order Sugeno fuzzy model with two rules may be 
used. 
Rule 1: If 5 is P
 and 6 is ‰
, then v
 = =
5 +  0
6 + >5 P 
 
Rule 2: If  is ! and 6 is ‰!, then v! = =!5 +  0!6 +  >! 
The system has five layers, as shown of Figure 7.3. 
 
Figure 7.3: First-order Sugeno ANFIS architecture 
Layer 1 (Input Module) 
Every node, , in this layer is an adaptive node with a node function. The output from each node '‡, 
will be given by Equation 7.1: 
'
'
,
= nP(5) for  = 1, 2 

, = n‰(6) 7.1  for  = 1, 3 
where 5 and 6 are inputs to node  and P and ‰ is a linguistic label associated with this node. 
Parameters in this layer are referred to as premise parameters. 
'‡, is the membership fPunction‰ o)f P and ‰ and specifies the degree to which the given 5 and 6 belong to the fuzzy set (  and   respectively. 
207 
 
 
Layer 2 (Rule module) 
Every node in this layer is a fixed node. The output is the product of all incoming signals. Thus, the 
output from this node is given by Equation 7.2: 
'!, = n‰(6)  ∗  n‰(6)  = 1, 3 7.2 
Each node represents the firing strength of the node. 
Layer 3 (Average module) 
E very node in this layer is a fixed node. The th node calculates the ratio of the firing strength of the th rule to the sum of the firing strengths of all rules, as represented by Equation 7.3: 
'3, = ¬ª¬¬« =  ª ª
 + ª!   = 1, 2 7.3 
The outputs (ª¬¬¬«) are called normalised firing strengths. 
Layer 4 (Consequent module) 
Every node in this layer is an adaptive node with a node function, given by Equation 7.4: 
'3, = ª¬¬¬«v =  ª¬¬¬«¬(=5 + 06 +  >) 7.4 
Where ¬ª¬¬« is the normalised firing strength from the previous layer 3. =,, 0 and > are set of 
parameters of the nodes. Parameters in this layer are called consequent parameters. 
Layer 5 (Output module) 
The single node in this layer is a fixed node which computes the overall output ('‚,) by summing all 
incoming signals. The node computation is given by Equation 7.5: 
'‚, =  ¬ª¬¬«v =  ∑∑ ª ªv  7.5 
7.2.1.3.2 Learning algorithm of the ANFIS 
The ANFIS can be trained using the hybrid learning algorithm presented by Jang (1993) where 
learning is done using two passes (forward and backward). In the forward pass, the algorithm uses 
the least squares method to identify the consequent parameters on layer 4. While in the backward 
pass, the errors are propagated backwards and the premise parameters are updated by gradient 
descent. Table 7.1 presents a summary of the activities in each of the two passes. 
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Table 7.1: Passes in the hybrid learning algorithm (Jang and Sun, 1995) 
 
Hybrid learning is used as it prevents learning from being trapped in local minima, which is a common 
problem of the gradient method of learning. This type of learning also increases learning speed, thus 
results can be obtained in a very short period of time compared to the neural network system. 
To illustrate the learning processes of the ANFIS, let us consider a network with  entries with one 
output. This system can be summarised by Equation 7.6: 
'BI=BI = (,  ) 7.6 
Where,  is the vector of input variables,   is the set of parameters and  is the function that 
implements the ANFIS. 
If there exists a function ) such that the composite function ).  is linear in some elements of   then 
these elements can be identified by the least squares method (LSM). This method is about estimating 
parameters by minimising the squared difference between the observed data and the desired data (Jens 
et al., 2012). 
If the parame ter set   can be decomposed in)to two se'tsB  I==BI  
 +  ! such that ).  is linear in the elements of !, then, by applying function  to the , Equation 7.6 can be transformed to 
Equation 7.7: 
). 'BI=BI = ). (,  ) 7.7 
Which is linear in the elements of  !. If values of  
 are given, then it is possible to plug  training 
data into Equation 7.7.  Here we have a mat rix equation of the form Pb = 6, where b is the unknown vector whose elements  are parameters in ! and which can be easily be solved using LSM. For each 
of the iterations (epochs) during learning, both forward and backward passes are done. 
Forward pass 
In the forward pass, an input vector and output are presented and the equation Pb = 6 is solved for 
each training set. This is repeated for all the training datasets and parameters  ! identified. After  ! 
is identified, the errors for each pair are computed. 
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Backward pass 
In the backward pass, the error signals propagate backwards and the premise parameters are updated 
using the gradient descendent. The derivative of the error measured with respect to each output is 
propagated from the output towards the input. 
The hybrid learning approach converges much faster by reducing the search space dimensions of the 
original back propagation method. The overall output is given by Equations 7.8:  
)v =  ª ª
 +
ª ª! v
 + ª
 +!ª! v! 
¬¬ v =  ª
¬¬¬¬(= 5 + 0 6 +  > )  +  ª¬¬¬¬(= 5 + 0 6 +  > ) 7.8 
v =  (ª¬¬«5)=
 +
«(¬¬ª¬
¬ 
«6)0
 + (¬¬ª¬¬«)

>
 +  (¬¬ª¬
«¬ !«5)=! + (¬
!¬ª¬¬ !«6)0! +  (¬¬ª¬¬«)>! 
Where =
, 0
, >
, =!, 0!, >! are linear consequent parameters. 
The least squares method is used to identify the optimal values of these consequent parameters. The 
least squares method (forward pass) is used to optimise the consequent parameters. The gradient 
descent method (backward pass) is used to optimise the premise parameters. The output of the ANFIS 
is calculated by employing the consequent parameters found in the forward pass. The output error is 
used to adapt the premise parameters by means of a standard back propagation algorithm. It has been 
proven that this hybrid algorithm is highly efficient in training the ANFIS systems (Jang and Sun, 
1997). 
The most widely used activation functions are the generalised bell function and the Gaussian function. 
These two functions are used because of their generally smooth character across the entire spread of 
data. They also have parameters that can be adjusted to suit the most desired membership function. 
The generalised bell function is given by Equation 7.9: 
n(5) = 1 + ­5 1−/ @­!®t  7.9 
The Gaussian function is given by Equation 7.10: 
n(5) = 5= ¯5 −/ @ ! Ž ° 7.10 
Where /, J and @ are parameters that represent the centre of the slope, and the centre and mean of 
the function respectively (Loganathan and Girija, 2014). 
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Learning with the back propagation neural network 
Derivatives of error are used for the back propagation learning. Let us consider a training dataset with 
p entries. The error of the =th entry can be calculated using Equation 7.11 which is given by:  
±
„ž = (;ž, − 'ž±,)! 7.11 

Where ;ž, is the th component of the =th target, 'ž±, is the th component of the actual output vector. 
The overall error will be given by Equation 7.12:  
}
„ =   „ž 7.12 

To implement the gradient descent of the error, the derivative of the error is calculated for each node 
output '. The error rate of the output node will be given by Equation 7.13:  
²„ž
²' = −2m;ž, − 'ž,p 7.13 ž,
If § is a parameter of the th node at layer *. Thus, the derivative of the overall error measure „ with 
respect to § will be given by Equation 7.14:  
²„ ²„
²§ =   ²§ 7.14 
The update formula for § will be given by Equation 7.15:  
∆§ = −³ ²„²§ 7.15 
Where ³ is the learning rate. The new § value (§M‘‹) will be calculated from the §‡© of the previous 
epoch and is given by Equation 7.16:  
§ = § − ³ ²„M‘‹ ‡© ²§ 7.16 
For the hybrid learning algorithm, each epoch has two passes, the forward and the backward pass. 
Equation 7.11 is applied to obtain the derivative of the errors from the forward pass. In the backward 
pass, these errors propagate from the output end towards the input end. The gradient vector is found 
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for all training data pairs and parameter weights (parameter connections) updated by the steepest 
descent Equation 7.16. 
An example to illustrate the hybrid learning of the ANFIS is given in Appendix 5. 
7.3 THE ANFIS SYSTEM FOR GROUNDWATER VULNERABILITY 
ASSESSMENTS: APPLICATION TO THE WITBANK, ERMELO 
AND HIGHVELD COALFIELDS 
Using the theoretical frame that has been discussed so far, an ANFIS hybrid system was developed 
in order to assess the groundwater vulnerability of the Witbank, Ermelo and Highveld coalfields. The 
hybrid system combines the fuzzy expert system and the artificial neural networks and tries to derive 
the best from these two powerful AI systems.  
7.3.1 Design Step of the ANFIS for Groundwater Vulnerability 
As mentioned before, the ANFIS is a hybrid system which combines artificial neural networks and 
the fuzzy expert system. The steps for using the ANFIS model for groundwater application includes: 
• selection of system training inputs and output values; 
• defining the fuzzy values for both inputs and outputs; 
• defining the fuzzy rules and, finally; and 
• creation and training of the artificial neural network. 
To implement and test the ANFIS a development tool is required. The Python Adaptive Neuro-Fuzzy 
Inference System algorithm developed by Meggs (2015) was used. A graphic user interface and a 
fuzzy membership design section were added to the algorithm for easy design and visualisation of 
the membership functions and the output model. 
7.3.1.1 Selection of system inputs and outputs 
The training inputs for the ANFIS system were the ten map layers of the SPT approach which showed 
a positive association when tested with high sulphate in the groundwater. The training output was the 
sulphate concentration in the groundwater similar to the procedure applied in the ANN training. Both 
the inputs and outputs were in vector format. According to Al-Hmouz et al. (2012), when selecting 
inputs, one must remove irrelevant inputs, and avoid using inputs which depend on other inputs. The 
model should be transparent. Given that, for the groundwater vulnerability assessment, the ten inputs 
were selected based on extensive research of how AMD interacts with the subsurface and given that 
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the spatial association test showed the region of each input to be spatially associated, all ten inputs 
were used to build the ANFIS model. 
7.3.1.2 ANFIS system training 
The ANFIS is a combination of the least-squares method and the back propagation gradient descent 
method applied to optimise and adjust the membership function parameters which would be used to 
generate the ANFIS model. The training input and output datasets are used to find values of the 
premise values for the membership function, as illustrated by the example in Appendix 5. Next, the 
threshold value is determined used to compare the actual output produced and the desired output. The 
least squares method determines the consequent parameters, and if there is a difference between the 
actual and desired output, the premise values are adjusted using the gradient descent method. This 
happens until the difference between the actual and the desired is minimal. At this stage, the ANFIS 
has been trained and is ready to predict an output based only the inputs. 
The membership functions for the ten input maps were designed using the same cognitive reasoning 
as that used for the fuzzy expert system. Figure 7.4 shows the membership functions of all ten input 
map layers. It is noteworthy that the membership functions for rainfall, clay content, hydraulic 
conductivity, depth to water table, rock-AMD reactivity and rock permeability constitute an 
increasingly positive function based on the conceptual model of groundwater vulnerability specific 
to AMD: the higher values of these parameters, the higher the vulnerability. For slope, surface 
sources, subsurface sources and pathways, the membership function is a steeper decreasing function 
which flattens after the threshold value in respect of the minimum value of the membership function 
has been reached. An increasing membership function was assigned to the clay and depth to water 
table parameters because low values of these parameters indicate where the groundwater vulnerability 
is highest. 
 
Figure 7.4: Membership functions used for the ANFIS system for a groundwater vulnerability 
assessment 
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After the membership function has been assigned to each of the ten map layers, the ANFIS algorithm 
is run for a given epoch value. Owing to the quick learning properties of the ANFIS there is no need 
to run an algorithm which determines the optimum number of epochs. One simply runs the ANFIS 
over 30 epochs and records the epoch value where the training error starts to increase. This value 
becomes the optimum number at which to terminate the training process. For the Witbank, Ermelo 
and Highveld coalfields, the ANFIS algorithm was run for 30 epochs and the results in Figure 7.5 
show that the training error decreased up to 20 epochs when the MSE error was at its minimum value 
of 0.23. After this point, the error started to increase. Thus, the optimum number of epochs was set at 
20 for this study area. The ANFIS algorithm was run again but this time with a cut off set at 20. This 
low number of epochs for which the system learns shows that the ANFIS could conceivably learn 
faster. Fast learning was achieved for the ANFIS as the selection of the ANN starting model from 
which it adjusts while running the iterations was obtained from the fuzzy membership functions 
which are also inputs to the ANFIS. 
 
Figure 7.5: Determining the cut-off epoch value for training the ANFIS system 
The minimum learning error obtained when the ANFIS was applied to generate a groundwater 
vulnerability model for the Witbank, Ermelo and Highveld coalfields was relatively higher because 
of the usage of the binary numbers which restricted learning to only ones and zeros. 
7.3.2 Hybrid System Model Results 
After training, the trained ANFIS system was used to determine the groundwater vulnerability values 
of the Witbank, Ermelo and Highveld coalfields at a spatial resolution of 30 x 30 m. The output from 
the ANFIS is a series of values at each of the map locations. In order to visualise these values, the 
data were interpolated using the kriging methods and the results reclassified into four classes (very 
214 
 
 
low, low, moderate and high) using the natural breaks method (ESRI, 2006). The results from the 
ANFIS are shown in Figure 7.6. The results show high groundwater vulnerability over the area 
between Ermelo and Carolina and the northwestern tip of the Witbank coalfield. Small areas south of 
Volksrust and Secunda are also marked by high values. The lowest values corresponded to the central 
part of the study area; otherwise, the rest of the study area was marked by low to moderate 
vulnerability. 
 
Figure 7.6: ANFIS groundwater vulnerability model of the Witbank, Ermelo and Highveld 
coalfields 
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Table 7.2 shows the aerial coverage sizes of the four groundwater classes, where the low vulnerability 
class has the largest size and the size distribution decreases as the vulnerability class changes from 
low to high with the high class covering the smallest aerial extent. Figure 7.7 shows a decreasing size 
of area with change in class from very low to low. 
Table 7.2: Aerial coverage of various vulnerability classes of the ANFIS model 
 
 
Figure 7.7: Aerial size distribution of the various groundwater vulnerability classes 
7.3.3 Validation of the ANFIS Model 
The ANFIS groundwater vulnerability model needed to be validated by another dataset which had 
not been used in the modelling. Three validation methods, namely correlation coefficient, cross-
section and geophysical methods were used in a similar fashion to the fuzzy and ANN models. 
7.3.3.1 Model validation using hydrochemistry data 
7.3.3.1.1 Correlation coefficient approach 
The correlation method for model validation involves a comparison of the model values with 
parameters which can be measured physically. This was done to determine the degree to which the 
model can accurately represent the real world. Some of the boreholes with measured sulphate 
concentrations which had not been used for model building were selected for validation purposes. 
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The ANFIS model values at each of these borehole locations were extracted. Sulphate was considered 
to be conservative in Chapter 3 and hence could be used as a possible tracer for AMD pollution. 
Figure 7.6 shows the spatial variation of sulphate concentration in the groundwater which was used 
for model validation (yellow circle with a black dot in its centre). The groundwater samples with a 
high sulphate concentration coincided with moderate to high groundwater vulnerability zones, while 
samples with low sulphate concentrations were located in low to very low groundwater vulnerability 
zones. 
A scatter plot (Figure 7.8) shows the relationship between the ANFIS model and borehole sulphate 
concentrations. The R value of 0.8216 was obtained between the ANFIS model values and AMD 
indicators (sulphate). This shows that the generated model correlates with sulphate in the groundwater 
as measured in the boreholes. 
 
Figure 7.8: Correlation scatter plots for sulphate against the ANFIS groundwater 
vulnerability model 
7.3.3.1.2 Validation using the cross-section method 
Hydrochemistry data from the National Groundwater Archive (NGA) database maintained by the 
DWS were verified by a field reconnaissance survey and the ionic balance checked. Only the samples 
with an ionic balance below 5 were used for model validation. A sulphate map was generated and a 
cross-section across the coalfield was plotted with values extracted along the cross-section. This was 
done both for the sulphate map and the ANFIS model. The sulphate concentration map is shown in 
Figure 4.21. 
The comparison between the map of sulphate concentrations and the vulnerability maps show that 
areas with high sulphate concentrations in the groundwater correspond to the highest vulnerability 
values whereas low concentrations indicate lower vulnerability areas (Figure 7.9). The differences at 
the start and end of the section (similar to the ANN model) were attributable to the scarcity of 
boreholes in this are causing gridding artefacts which normally affect the edges of the gridded data 
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as explained in ANN, Chapter 6. Excluding the edges of the profile line, the model values generally 
decrease from the Witbank coalfield towards the Ermelo coalfield corresponding to changes in the 
sulphate profile values. 
 
Figure 7.9: Profile along cross-section A–B showing the DWS borehole sulphate 
concentrations and the ANFIS vulnerability model profile 
7.3.3.2 Validation using geophysical techniques 
The geophysical survey results described in Chapter 4, section 4.5.4.2 were used to validate the 
ANFIS groundwater vulnerability model. From a comparison of the porosity ranges for the 
unsaturated zones of the four sites and their corresponding model values it can be seen that, where 
the porosity values are high, the model values are also high (Table 7.3). Using the observations at the 
four sites, the areas with high porosity values correspond to areas characterised by high groundwater 
vulnerability values. There is a clear leap in high porosity range values and the low porosity range 
coinciding with a leap in the model values owing to the usage of binary data to generate the ANFIS 
model. (Table 7.3). With regard to the seismic velocity, low seismic values correspond to high model 
values and high seismic values corresponds to low model values. A possible explanation for this 
relationship is given in section 4.5.4.2 discussing the validation of the fuzzy model using seismic 
survey data. 
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Table 7.3: Comparison of derived porosity values and ANFIS groundwater vulnerability 
model values for each of the survey sites 
 
7.4 DISCUSSION 
The ANFIS used in this chapter belongs to the hybrid branch of AI which combines machine learning 
and a fuzzy inference system. When designing the ANFIS model, the fuzzy memberships were 
subjectively assigned but due diligence was done to ensure that most of the information with regard 
to AMD generation, transport and attenuation processes were used sparingly. This was done similarly 
to the fuzzy modelling in such a way that the models can be used at a regional coalfield scale. The 
ANFIS uses the fuzzy membership function and adjusts the input-output relationship by learning from 
the data in a similar fashion as the ANN. Thus, the ANFIS as a hybrid model produces an output 
groundwater vulnerability model that resembles both the fuzzy and ANN models. 
The learning rate of the ANFIS was very fast, only requiring 20 epochs (compared to 8 770 epochs 
for the ANN). This was attributable to the hybrid learning algorithm used by the ANFIS which is a 
combination of the gradient descent learning of the ANN and the least squared method which 
increases the learning speed considerably. 
The results for the ANFIS correlated very well with sulphate which may be explained as follows: 
• The choice of parameters (S, P and T) and the allocation of appropriate fuzzy memberships for 
each input map layer were appropriate to the ANFIS for modelling AMD migration processes 
at a regional scale. 
• The ANFIS was trained in such a way that the readjusted weights which connect the inputs to 
the output through a hybrid learning process was able to mimic the general human thought 
process with regard to groundwater vulnerability. For example, in Chapter 3, it was learnt that 
sulphate is conservative and that its concentration in the groundwater may be an indication of 
loading of sulphate from the surface or near surface. Thus, high sulphate would translate to high 
groundwater vulnerability. The ANFIS model values correlated with sulphate values which is 
a good indication that the ANFIS was well trained to possibly mimic human thought. 
A limitation of the ANFIS (hybrid) system is that, unlike the ANN system, the membership functions 
needs to be defined for the ANFIS system to be implemented. This could be a problem if the system 
219 
 
 
to be modelled is not well known; hence, the ANNs are the more popular machine learning tools in 
AI applications. 
7.5 SUMMARY 
The ANFIS was developed and successfully used to generate a groundwater vulnerability model of 
the Witbank, Ermelo and Highveld coalfields where the model showed a strong correlation with 
borehole sulphate concentrations from two different datasets (DWS dataset and unused data from the 
2013 sampling programme). Seismic velocities and porosity estimated from geophysical surveys also 
showed a linear relationship, where highly vulnerable areas were found to be associated with the 
subsurface with relatively higher seismic velocities and higher porosities derived from resistivity 
surveys. 
Thus, knowledge-, data-driven and hybrid AI systems assessment tools were developed and 
successfully applied to the Witbank, Ermelo and Highveld coalfields. A toolbox in the form of a 
simple graphic user interface with all these AI tools will go a long way in assisting both AI and non-
AI experts to successfully use these tools for groundwater vulnerability assessments of AMD at a 
coalfield scale. 
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CHAPTER 8: TOOLBOX FOR RAPID ASSESSMENT OF 
GROUNDWATER VULNERABILITY 
8.1 INTRODUCTION 
The previous chapters dealt with the development of the SPT groundwater vulnerability approach 
which was implemented using various artificial intelligence algorithms (fuzzy expert system, ANNs 
and ANFIS) in the generation of various groundwater vulnerability models. The models include 
knowledge-driven, data-driven and a hybrid system. In order to assist in the rapid generation of 
groundwater vulnerability AI models, a semi-automatic program “toolbox” was developed where all 
the tools developed in this research are found and will be described. All the AI models in this thesis 
were developed using the groundwater vulnerability tools from this toolbox. The user manual for the 
toolbox is found in Appendix 3. 
8.2 OVERVIEW OF THE TOOLBOX 
The toolbox was developed using Python open-source programming language and is entitled the 
“Groundwater Vulnerability Artificial Intelligence” (GVAI) toolbox. The toolbox is built using 
several Python built-in libraries: Tkinter, Numpy, Matplotlib, Osgeo and Pandas. Figure 8.1 presents 
an overall systems overview of the GVAI toolbox which summarises the tools developed in the 
current study. 
The toolbox (program) accommodates the ten input raster data of the SPT groundwater vulnerability 
assessment and if data on polluted sites are available, three models (fuzzy expert system model, ANN 
model and the ANFIS mode) can be generated using the program. Conversely, if no polluted sites are 
known, only the fuzzy expert system model will be generated. The resultant models are georeferenced 
rasters which can be viewed or processed on any GIS program and print-ready jpeg images can also 
be produced. 
The program starts by prompting the user to load the ten input map layers (rainfall, topographic slope, 
distance to surface sources, distance to subsurface sources, soil clay content, distance to pathways, 
rock permeability, aquifer hydraulic conductivity, depth to water table and rock-AMD reactivity) as 
defined by the SPT approach to groundwater vulnerability at a coalfield scale. 
Once all the map layers have been loaded into the program, the user is able to view the map before 
proceeding to the other steps or modules. If it is possible to view the data, then the data are in the 
correct format for the programs otherwise the user has to correct the maps before proceeding. 
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Figure 8.1: Systems design flowchart of the groundwater vulnerability (GVAI) toolbox 
Once the map layers have been loaded, the program asks whether a polluted site dataset is available. 
If no such data are available only the knowledge-driven fuzzy expert system module is enabled. 
However, if the required data are available, two buttons representing the knowledge-driven approach 
(fuzzy expert system) and the data-driven approaches (ANN and ANFIS) are enabled. To run the 
knowledge-driven fuzzy expert system no polluted sites are required, but for the data-driven systems 
(ANN and ANFIS), polluted and non-polluted sites are required as training data points. 
The GVAI software comprises seven modules: 
1. main menu module which initialises the program; 
2. data input module where data are loaded into the program; 
3. fuzzy expert system module which executes the multistage fuzzy inference network; 
4. data-driven data pre-processing module which executes spatial association tests and 
generates binary maps for data-driven AI modelling; 
5. data-driven ANN module which executes the ANN algorithms to generate a groundwater 
vulnerability model; 
6. data-driven ANFIS module which executes the ANN algorithms to generate a groundwater 
vulnerability model; and 
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7. the model comparison module which does a statistical comparison of the various models 
using a set of validation points. 
8.2.1 Main Menu Module 
This module is the main window which launches the program and from where the help files can be 
accessed (Figure 8.2). 
8.2.2 Data Input Module 
This module is where all the datasets that are required for modelling are fed into the program. First, 
the user loads each of the ten map layers rasters using the corresponding browse button and inspects 
the map by clicking the corresponding “plot” button (Figure 8.3). Once all the ten maps have been 
added to the program, the program asks whether groundwater pollution vector data are available. If 
the answer is “YES” then the borehole point “browse” and “plot” buttons are enabled prompting the 
user to load the data into the program. At the same time, the previously disabled knowledge-driven 
approach (fuzzy expert system) and data-driven approaches (ANN and ANFIS) buttons are enabled. 
Thus, with the ten maps and pollution data loaded, the user can execute both the knowledge and data-
driven approaches. Alternatively, if the answer is “NO”, then only the knowledge-driven approach 
(fuzzy expert system) can be performed. 
 
Figure 8.2: Main menu module window 
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Figure 8.3: Input module window 
 
Figure 8.4: The “about” window, showing the software details 
8.2.3 Fuzzy Expert System Module 
The fuzzy expert system module accepts all ten map raster layers from the input data module. The 
module allows the user to design the fuzzy membership function for each map layer according to 
expert knowledge on AMD processes in the area under study. The user is also able to execute 
automatic processing which relies on parameters values as outlined in Sakala et al. (2018). When 
designing the fuzzy expert system, the drop-down buttons are used to select values for various map 
values (H), confidence (@v), @_H/5 and @_H7 for each of the corresponding map layer. The @_H/5 
value specifies the maximum value of u and the @_H7 value specifies the minimum value of u 
according to Equation 4.2. The program then uses these values to generate the fuzzy values of each 
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map layer by executing Equation 4.2. The fuzzy membership functions for the slope, surface sources, 
subsurface sources and pathway are step functions where the user is required to specify a threshold 
value. Once all the design parameters have been adjusted, the program converts the raster inputs into 
fuzzy values and results can be viewed by clicking on the corresponding “plot” button. Figure 8.5 
shows the process flow for the fuzzy expert system that starts with data input, after which the user 
defines the design parameters and operators and ultimately generates the output fuzzy model. This 
process flow is converted into a simple graphic user interface (GUI), as shown in Figure 8.6. 
Once all the map layers have been converted to fuzzy values, the user then specifies the fuzzy 
operators (AND, OR, PRODUCT, GAMMA, SUM) accordingly. For example, any of the surface or 
subsurface sources of AMD pollution can contribute to groundwater vulnerability, hence the “OR” 
operator may be selected. Once all the user-defined parameters and operators have been specified, 
the program runs the fuzzy inference engine and produces output map layers for each operation. The 
user is then prompted to choose three map layers (sources, transportation pathways and traps) which 
will be combined to generate the final fuzzy groundwater vulnerability model. 
 
Figure 8.5: Fuzzy expert system flow chart 
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Figure 8.6: Fuzzy expert system module window 
8.2.4 Data Pre-Processing Module for Data-Driven AI Systems 
In order to execute the data-driven AI approaches, the datasets are first pre-processed in the pre-
processing module (Figure 8.7). Two pre-processing steps are executed where each of the ten map 
layers are tested for spatial associations and regions that show over 50% of the high sulphate 
concentration in groundwater obtained. The steps are clearly outlined in section 5.3.1. When the test 
button is clicked, the program runs the spatial association test and outputs a graph showing the 
cumulative frequency curve compared to high sulphate borehole locations. 
From the graph produced after clicking the “test” button, the user can identify the region range of 
each map layer where more than 50% of the boreholes with high sulphate concentrations are found. 
After the spatial association test have been done for all ten of the map layers, the identified region 
ranges values are entered on the binary creation section. In the binary creation section, the user enters 
the low (P‡‹) and high (P¢¡¢) threshold values identified in the spatial association test section for 
each map layer. The program then reclassifies the map layer value (H/=…Ÿ‡†‘ ) into binary format 
(6®) according to Equation 8.1:  
6 =  – 1 v P‡‹  ≤ H/=…Ÿ‡†‘ ≤ P¢¡¢ ® 0 v H/=  8.1 …Ÿ‡†‘ >  P‡‹ /7 H/=…Ÿ‡†‘ <  P‡‹
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Figure 8.7: Data-driven artificial intelligence data pre-processing module window 
The results may be viewed by clicking the corresponding plot binary map button on the extreme right-
hand side of the module window. Once all binary maps have been created and viewed as correct, the 
“produce the training dataset” button is clicked and the program creates all the necessary files for 
running the ANN and the ANFIS algorithms. In order for this to be done, the program also needs to 
extract all the values for each of the cells covering the study area for each from the binary map layers 
generated in the pre-processing module. This is done by another algorithm designed to extract the 
unique combinations of the input map layer. The unique combination file with all the input data 
combinations is created. 
Upon clicking the “produce the training dataset” button, the previously disabled “go to artificial 
neural networks module” and “go to adaptive neural-fuzzy inference system module” are enabled. 
The user can now click on either of these options to access these modules. The “return to home page”, 
“help” and “about” buttons are discussed above. 
8.2.5 ANN Module 
The ANN module receives data from the pre-processing module and computes the groundwater 
vulnerability model using the ANN algorithm. Figure 8.8 shows the flow chart of the ANN processing 
module and its connection to the data input and the data pre-processing modules. The module has an 
algorithm which considers the input data distribution and number of points in determining whether 
to use the tenfold stratified or the leave-one-out cross-validation approach. The module allows the 
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user to run the ANN model in manual or automatic mode (Figure 8.9). When manual mode is selected, 
the user is prompted to specify the training parameters (number of neurons in the hidden layer, epochs 
(iterations) and activation function) and the ANN model is generated using these parameters. After 
training, the training error graph is produced, showing how the training has progressed. 
 
Figure 8.8: ANN system flow chart showing the relationships of various algorithms 
228 
 
 
 
Figure 8.9: ANN module window 
When the automatic mode is selected, data from the pre-processing module are fed into the epochs 
and hidden layer neurons determination algorithms. The algorithms are described in 5.3.2. Once the 
optimum number of epochs and number of neurons in the hidden layer has been determined, these 
parameters become the setting for the tenfold or leave-one-out training/validation algorithms which 
are explained in detail in 5.3.2. The best-trained network from either the tenfold or leave-one-out 
training/validation algorithms would be suitable for the prediction/classification of the entire study 
area. The trained network/system is then used to predict/classify the output values for each of the map 
cells. After the operation has been carried out, the training graph is produced and displayed. 
The resultant from the prediction/classification is then reclassified into groundwater vulnerability 
classes using the natural break method (ESRI, 2006) and the module stops after the model has been 
generated. 
8.2.6 ANFIS Module 
The process flow (Figure 8.10) for the ANFIS system is almost similar to that of the ANN system 
described earlier. The only difference is that for the ANFIS system no hidden layers are determined 
as the ANFIS system replaces the hidden layers with membership functions. The ANFIS module 
allows the user to design the ANFIS membership functions for each of the map layers by specifying 
the Gaussian sigma and mean values and the resultant functions can be viewed. The program is only 
capable of executing the Gaussian function. Figure 8.11 shows the GUI for the ANFIS module. 
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Figure 8.10: ANFIS expert system flow chart 
When the button “run ANFIS using defined settings” is clicked, the ANFIS algorithm is run using 
these defined functions. The resultant model is produced and displayed together with the training 
error graph. 
The module allows the user to run the ANFIS algorithm using the settings that the program would 
have calculated using the pre-set setting. In this mode, the user has no control over the membership 
functions as the program would use pre-defined values with consideration of the possible data ranges 
of each map. 
230 
 
 
 
Figure 8.11: ANFIS module window 
8.2.7 Model Validation Module 
The model validation module (Figure 8.12) is a section when the AI models generated are statistically 
validated using a separate validation vector dataset. The module prompts the user to select the models 
using the “browser” button. The user can view the model by clicking the “plot” button for the 
corresponding model. The main aim of groundwater vulnerability mapping is to classify a large area 
into relative classes. Thus, the best model is one which is able to predict precisely polluted sites which 
were not used in the modelling process. Normally the worst-case location in respect of pollution is 
used in this module for validation. Pollution-area graphs are produced for each model and used to 
select the best model with the highest correlation value. 
 
231 
 
 
 
Figure 8.12: Model validation module 
8.3 DISCUSSION AND SUMMARY 
One of the research problems is the development of tools for a rapid assessment of groundwater 
vulnerability which does not significantly compromise the accuracy of the results. Hence, AI systems 
with proven success in solving similar problems were used in the development of the toolbox. 
By doing several trials with machine learning (ANN, ANFIS) algorithms it was realised that if 
training is done using binary maps generated by assigning binary values (1) to cover 100% of the 
training points there is a large validation error. However, if between 50 and 100% of the training 
points are used, the validation error is lower. Thus, for machine learning to be effective for 
classification or prediction, noise in the data is important for the trained model to be generalised. This 
increases the system generalising capabilities for the classification or prediction of new data that were 
not used in the training process. 
The Groundwater Vulnerability Artificial Intelligence toolbox developed is a simple to use program 
which runs complex algorithms in the background. The user interface proved to be quite easy to use 
for non-AI experts but it is recommended that the user must have at least some background of 
groundwater vulnerability and /or acid mine drainage systems. 
The program, which is a stand-alone program dedicated to groundwater vulnerability assessments 
specific to AMD at a coalfield scale, accelerates the generation of models because only the necessary 
functions are included. The generated models can be redone as more information or higher-resolution 
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data become available. Future modification of the program includes an option to save the settings so 
that they can be accessed in future or at the next program start-up. 
Using binary maps for machine learning reduces the amount of data to be constrained within the 
current limits of random access memory of a personal computer. However, this limits the 
classification or prediction to a binary output. 
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CHAPTER 9: CONCLUSIONS AND RECOMMENDATIONS 
9.1 CONCLUDING REMARKS 
The research involved critically analysing available groundwater vulnerability approaches and AMD 
pollution to develop a specific approach applicable to a typical coalfield by incorporating AI to 
enhance the human capabilities in the assessment of groundwater vulnerability. Laboratory and field 
experiments were done and results used in the selection of appropriate groundwater vulnerability 
input map layers and for validation of generated vulnerability models. To complement and summarise 
the research findings, a simple-to-use graphic user interface toolbox was developed which contains 
the rapid assessment tools for a groundwater vulnerability assessment of a typical coalfield. The 
Witbank, Ermelo and Highveld coalfields of South Africa which are Karoo sedimentary-hosted coal 
deposits was used as a case study from which the developed groundwater vulnerability approach and 
toolbox were tested. 
9.1.1 Development of AMD Specific Groundwater Vulnerability Approach  
An analysis of the three approaches of groundwater vulnerability (index and overlay, process-based 
modelling and statistical) identified that each has its own strengths and weaknesses. Using the 
analysis of these conventional approaches and inspiration gained from the globally accepted mineral 
systems process-based workflow for mineral prospectivity analysis, the petroleum systems and the 
source-transport-attenuation approaches, an approach (SPT) was developed which offers a holistic 
approach for the assessment of groundwater vulnerability to AMD at a coalfield scale. This was done 
by combining factors based on pollutant sources, energy that drives the pollution migration and ways 
in which AMD interacts physically and chemically with the subsurface. The approach is a hybrid 
approach built with the following characteristics from the three vulnerability approaches: 
• built on readily available datasets to interpret an output groundwater vulnerability model that 
can be used by non-scientists or hydrogeologists (extracted from index and overlay 
approaches); 
• incorporation of the processes in terms of which AMD interacts with the subsurface (extracted 
from process-based approaches); and 
• inputs combined using appropriate statistical tools such as AI systems in this research (extracted 
from statistical approaches). 
Parameters which were extracted from popular approaches such as DRASTIC include: depth to water 
table, aquifer hydraulic conductivity, rainfall which was replaced by recharge, soils and topographic 
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slope. Other parameters which were incorporated in the assessment included those which are specific 
to AMD pollution such as surface and subsurface sources of pollution, rock-AMD reactivity, 
pathways and rock permeability. The input map layers were joined together using AI. The SPT was 
successfully applied to the Witbank, Ermelo and Highveld coalfields. 
9.1.2 Laboratory and Field Experiments for Groundwater Vulnerability 
Input Selection and Model Validation 
Laboratory work done involved a simulated experiment where AMD from a typical coalfield was 
subjected to soils of varying clay content and it was found that soils with a high clay content, greater 
than 31%, were able to reduce iron concentrations and removed sulphates to an extent. The 
concentration of calcium and magnesium increased in the leachate. An ionic exchange reaction was 
identified as a possible cause, where the acidic environment causes iron to displace calcium and 
magnesium from soil particle exchange sites and occupies their position resulting in a decrease in 
iron and an increase in calcium and magnesium. Aluminium concentration remained unchanged in 
the leachate because their ions are tighly held on exchange sites owing to their high exchange affinity. 
Other laboratory work done was a column leach experiment under saturated and unsaturated 
conditions with the aim of understanding how various rocks respond in an AMD environment. In this 
experiment, AMD from a typical coalfield was reacted with various rocks found in a typical Karoo 
coalfield over a period of 91 days and leachate was collected and analysed. An analysis of the leachate 
revealed interesting findings: 
• Dolomite was able to neutralise the pH within the first seven days and maintained a neutral pH 
till the end of the experiment. At the time when the pH became neutral, AMD heavy metal 
pollutants (aluminium, iron and manganese) were removed from the AMD solution, whilst the 
concentration of calcium and magnesium in the leachate increased. Dolomite dissolution 
processes are responsible for these observations. 
• Rocks with plagioclase such as diabase and dolerite were also able to neutralise pH and remove 
AMD heavy metal pollutants (aluminium, iron and manganese) but this effect only lasted for a 
few weeks. 
• Other rocks dominated by quartz minerals were not able to significantly affect the pH and hence 
the AMD heavy metal pollutants were not removed. 
• The order in which rocks attenuated AMD in a typical Karoo coalfield was found to be in the 
following order: dolomite, dolerite, mudrock, diamictite and sandstone, which can be expressed 
in terms of mineral composition as carbonate, plagioclase, chloride and quartz, where the 
235 
 
 
dissolution of minerals also follows this sequence. The sequence was used to rank rocks 
according to the removal of AMD heavy metal pollutants. 
• The chemical parameters which can be used as possible natural tracers for an AMD-specific 
groundwater vulnerability assessment are sulphate and chloride concentrations. This was 
obtained from the column leach experiment where it was discovered that sulphate and chloride 
concentration remained unchanged for various typical coalfield geological formations and over 
a time period of 91 days when rocks had been subjected to AMD under saturated and 
unsaturated conditions. 
• The column leach experiment showed that the reactions between AMD and rock masses are 
more pronounced in the unsaturated zone than the saturated zone, showing the role played by 
the presence of oxygen in the attenuation of AMD in the subsurface. 
Fieldwork done involved the collection of water samples from boreholes within the Witbank, Ermelo 
and Highveld coalfields, which were analysed for hydrochemistry. The results revealed two water 
types, one due to natural weathering processes showing very early stages of water-rock interaction 
and another showing signs of enrichment of sulphate which was interpreted to be attributable to 
human activities such as coal mining.  
In the research, ground geophysical surveys that were conducted found that resistivity and seismic 
refraction survey results in the form of porosity and seismic velocities correlated well with all the 
three AI generated groundwater vulnerability models for the Witbank, Ermelo and Highveld 
coalfields. Thus, these methods can be used to validate groundwater vulnerability models, but the 
surveys need to be done at many sites and on similar geological formations. This would reduce the 
ambiguities in geophysical interpretations and minimise the effect of geological variations which can 
affect the geophysical response. This would leave only the hydrogeology properties, which may be 
compared with interpreted geophysical responses at various groundwater vulnerability classes. 
9.1.3 Application of AI to the Assessment of Groundwater Vulnerability 
Specific for Coalfields 
Three groundwater vulnerability assessment tools were developed, the knowledge driven fuzzy expert 
system, data-driven artificial neural network and the hybrid adaptive neural-fuzzy inference system. 
The fuzzy expert system, a knowledge-based system, is solely dependent on the expert’s cognitive 
reasoning on the AMD pollution transport and attenuation and was able to produce a groundwater 
vulnerability model which was highly correlated (	 = 0.809) with sulphate concentration. The ANN 
which belongs to the data-driven AI with topology 10-9-1 was trained for 8 770 epochs and was able 
to generate a groundwater vulnerability model which was highly correlated (	 = 0.909) with sulphate 
236 
 
 
concentrations. Lastly, the ANFIS, which is a hybrid system made by combining the fuzzy expert 
system and ANN, was trained using a hybrid training algorithm and also generated a groundwater 
vulnerability model which was closely correlated (	 = 0.8216) with groundwater sulphate 
concentrations. While any of the models can be used, the ANN had the highest correlation with 
sulphate concentrations in groundwater. 
This gives the users of the tools options in regard to which of the three tools to use. At the same time 
the validation results for each model can be used to assist in making the decision as to which model 
to select. The three groundwater vulnerability tools produced different models, but with remarkably 
similarities at a regional scale. All three models were fairly consistent with field realities in the form 
of geophysical responses and hydrochemistry datasets. 
9.1.4 Groundwater Vulnerability Graphic User Interface Toolbox 
The rapid groundwater vulnerability assessment tools generated by the research were packaged into 
a toolbox which contains all the tools needed for the AI modelling of groundwater vulnerability. The 
program is called the “Groundwater Vulnerability Artificial Intelligence (GVAI)” toolbox and works 
in both manual and semi-automatic mode, where on all the options, the user can contribute to the 
decisions taken in the modelling process. Tedious processes which are normally done by trial and 
error have been automated to assist the user in the production of groundwater vulnerability models at 
high speed and improved accuracy. The program is also flexible in the sense that if a map layer is 
changed the user can quickly update the model. 
9.2 RECOMMENDATIONS 
9.2.1 General Recommendations 
The recommendations on the interpretation of the groundwater vulnerability models in a language 
understandable by policy and decision makers are summarised as shown in Table 9.1. This 
simplification goes a long way in the development of water resource management models and in 
facilitating their incorporation into a water-resource management decision-making process. 
237 
 
 
Table 9.1: Recommendations for the management of the water resources of the Witbank, 
Ermelo and Highveld coalfields 
 
9.2.2 Limitations of the Developed Data-Driven Approaches 
The vulnerability approaches developed make use of sulphate concentrations mainly because of their 
observed conservative nature in saturated and unsaturated conditions from the soils batch leach, rock-
AMD reactivity column leach experiments and supported by findings by Li et al. (2006) and Bottrell 
et al. (2008). Sulphate concentrations in groundwater were used both for modelling and validation 
from data collected by sampling several boreholes. Analytical errors emanating from field water 
238 
 
 
sampling, water sample preparation and laboratory analytical analysis cannot be ruled out and are 
often difficult to quantify accurately. Hence, the produced models include these inherent uncertainties 
even though water quality tests were done and results showed an acceptable ± 5% ionic balance. 
9.2.3 Recommendation for Future Work 
The approach developed in this research opens up more avenues for its application in generating 
groundwater vulnerability models for other pollutant sources such as nitrates, landfill, domestic, 
industrial and mining areas. The developed approach was only tested for three coalfields in South 
Africa and more vigorous testing and validation of similar or different coalfields need to be done to 
determine the robustness of the methodology to different hydrogeological conditions. However, 
based on the conceptual model and the adaptive nature of the developed tools, it is anticipated that 
the correct groundwater vulnerability models will be generated for other coalfields as well. 
Complex learning algorithms such as deep learning, currently used for data mining of very large 
datasets ranging from internet search engines, speech recognition and image processing, can be tested 
for their applicability to the generation of groundwater vulnerability models for very large areas at a 
high resolution. 
Incorporation of groundwater flow information into the model design can be considered as the SPT 
approach developed in this research only focussed on the vertical migration of AMD and its 
interaction with the subsurface. In nature, pollution also migrates laterally in a three-dimensional 
space in a process which is quite complex where fractures also need to be mapped and incorporated 
into the model. Such an approach is likely to make the modelling expensive as fractures are small and 
mapping them over large area will require closely spaced borehole density data. Pump testing would 
need to be carried out. However, for an area as large as the present study area, it is believed that these 
measures are not necessary as the results are meant to produce a relative comparison of various areas 
in terms of groundwater vulnerability rather than a precise AMD migration modelling at a local scale. 
 
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253 
 
 
APPENDICES 
APPENDIX 1: SOIL BATCH LEACH EXPERIMENT 
Appendix 1.1 Results of leachate analysis after the soil batch leach with AMD 
 
Appendix 1.2 Results of leachate analysis after the soil batch leach with de-
ionised water 
 
Appendix 1.3 Results of major elements of soil samples analysed by XRF 
 
 
 
254 
 
 
APPENDIX 2: ROCK-AMD COLUMN LEACH EXPERIMENT 
Appendix 2.1 Results of chemical analysis of leachate under saturated conditions 
 
 
 
 
Appendix 2.2 Results of chemical analysis of leachate under unsaturated 
conditions 
 
 
 
 
Appendix 2.3 Results of the mineralogical analysis of rock samples by XRD 
 
Appendix 2.4 Results of the XRF analysis of the major elements of rock samples 
 
 
APPENDIX 3: DETERMINATION OF OPTIMAL DATA-DRIVEN MODEL 
PARAMETERS 
Appendix 3.1: Epoch determination algorithm for data-driven approaches 
Binary map data are feed into a data-driven AI algorithm where training is carried out at various 
training iterations (epochs) and a fixed initial number of neurons in the hidden layer for ANN training. 
No number of neurons in the hidden layer is specified for the ANFIS system. The initial number of 
neurons in the hidden layer for ANN modelling may be determined by multiplying the number of 
inputs by two and adding one according to a simple rule formulated by Shigidi and Garcia (2005). 
Thus, in the case of ten input layers, the initial number of neurons in the hidden layer is 21 (from 
calculation: 10 x 2 + 1). This value is used for initialising the ANN but will be optimised by the 
hidden layer, determining the algorithm which will be executed once the optimum number of epochs 
has been determined. 
255 
 
 
For each training epoch, the data-driven AI ivs trained and used to determine the output values of each of the tr6aining points. The predicted value ( ‘) from the data-driven AI is compared with the actual values ( ‘) and the error returned is for each trEai n„ing point. The errors are then combined for each Eep o„ch and a mean square of errors (MSE) ( ‘žµ¢) for each training epoch recorded. The ‘žµ¢ value for each training epoch is calculated using Equation A1 (De Oliveira et al., 2011): 
E „ ‘žµ¢ =  R1 
(v‘ − 6‘)! A1 
Where R represents the number o f data points, v‘ is the value predicted by the program and 6‘ is the actual value for the data point . 
A graph of each epoch training value and the Eco r„responding E „‘žµ¢ values is produced (Figure A1). The epoch train Eing value with the lowest ‘žµ¢ vEal u„e is returned as the optimal number of epochs (M) such as ! in the example in Figure A1. The ‘žµ¢ is also called the “error rate”. 
 
Figure A1: Determining the optimum number of epochs with minimum validation MSE 
Appendix 3.2: Hidden layer neuron number determination algorithm for data-
driven approaches 
Using the optimum number of epochs (M) as fixed, the ANN algorithm is run with varying number 
of neurons in the hidden layer. For each neuron hidden layer training step, the ANN is used to 
determine the output values of each of the training points. The predicted value (v¢) from the ANN 
network is compared with the actual values (6¢) and the error (v¢ − 6¢) is returned for each training 
256 
 
 
pEoi n„t. The errors are then combined for each number of neurons in the hidden layer and an MSE ( ¢©©‘M) for each number of neurons in the hidden layer is recorded. The E „¢©©‘M is calculated 
using Equation A2 (De Oliveira et al., 2011): 
E „¢©©‘M =  R1 
(v¢ − 6¢)! A2 
Where R the number of  data points is, v¢ is the value predicted by the program and 6¢ is the actual value for the data point . 
A graph of each number of neurons in the hidden layer and the corresponding E „¢©©‘M values is 
produced. The number of neurons in the hidden layer with the lowest E „¢©©‘M value is returned as 
the optimum number of neurons in the hidden layer (H), such as )3 in the example in Figure A2. 
 
Figure A2: Determining the optimum number of neurons in the hidden layer with minimum 
validation MSE 
Appendix 3.3: Data splitting algorithms 
Using the optimum number of hidden layer neurons (H) and epochs (M), the data-driven (ANN or 
ANFIS) algorithm modelling can be done. First, an assessment of the method/technique for validation 
needs to establish if the resultant models are scientifically defensible. 
With access to an unlimited number of examples (training points), models can be generated by simply 
choosing the model with the lowest error rate. However, in real applications, for example, using 
borehole data over a given area, only a finite set of points are available for training, and therefore 
257 
 
 
other approaches need to be devised (Makarevich, 2015). One approach is to use the entire dataset 
for training to generate the model and then to estimate the error in predicting the same points which 
were used for the training. However, this naive approach is likely to over-fit the training data in the 
final model. That is, the model will accommodate the training data but usually fail to predict/classify 
new data after the training process (Makarevich, 2015). The trained model is intended to be a 
generalised model so that it can accommodate irregularities and variations in future data that will be 
used for predications classification. In addition, the performance of the model is unknown as no 
known points were kept and used for validation. This problem can be solved by cross-validation, 
which is a process whereby the dataset is split into three distinct subsets for training, validation and 
testing (Makarevich, 2015) (Figure A3). The training dataset refers to a set of examples (points) used 
for learning to fit the parameters of the model. The validation dataset is a set of examples (point) used 
to fine-tune the model. The testing dataset comprises a set of examples (points) used only to assess 
the performance of a fully trained model. After assessing the final model with a test dataset, no further 
training is done. There are various ways to split datasets, with the most commonly used techniques 
being: 
• holdout method; 
• random subsampling; 
• k-fold cross-validation; and 
• leave-one-out cross-validation. 
 
Figure A3: Illustration of three way data splitting 
258 
 
 
Holdout method 
In this technique, the dataset is split into training, testing and validation datasets, where a small 
portion of the data are selected for testing and the rest divided into a training-validating dataset (Figure 
A4). This approach is a once off train-validate experiment (Remesan and Mathew, 2014). The dataset 
is split into training/validation according to proportions decided by the expert, for example: 70/30, 
75/25, 80/20 (Iqbal and Rizwan, 2009; Ignacio et al., 2013; Gholami et al., 2015). 
 
Figure A4: Holdout method splitting the dataset into training, validation and testing sets 
Training is then done and the trained model used to predict/classify values of the validating dataset 
to obtain the validation error. This model is then assessed by predicting/classifying values of the 
testing dataset to obtain the performance of the model. 
Problems arise when the dataset is sparse and the researcher cannot afford to set aside a portion of 
the dataset for validation or testing. Another problem that can occur is when the split between training 
and validation is inappropriate or unfortunate. Despite these drawbacks, this method is used by 
several authors (Iqbal and Rizwan, 2009; Ignacio et al., 2013; Gholami et al., 2015) for its fast 
computation time as the training/validation process is a single operation. 
This technique raises the question as to which splitting proportion is considered correct or best as the 
split is determined by the expert running the models and the accuracy of the resultant model is often 
questionable. Another consideration is which points to select as training points and which as 
validation datasets. These problems, related to the holdout method, can be solved by the random 
subsampling technique. 
Random subsampling 
In this approach, the data are split into two smaller groups, one for training-validation and the other 
for testing. The training-validation dataset is then randomly split further into a small portion for 
validation and the remainder for training. Training is done using the training dataset and the trained 
model used to predict the values of the validation dataset is termed experiment 1. The training-
validation dataset is then split randomly again, but this time using a different random combination to 
that used in experiment 1, constituting experiment 2. This process of splitting the training-validation 
dataset continues until all the possible random combinations have been used, after which the 
259 
 
 
combination with the lowest validation error is selected as the best model (Figure A5). This best 
model will then be assessed for its performance by using it to predict/classify values of the test dataset. 
This technique produces better results than the holdout technique. The results from the approach 
where examples (points) are chosen randomly are also still debatable, as the random selection is not 
repeated in the event that one wants to run the model again. Thus, the model generated using randomly 
generated training/validation splitting is barely repeatable and may cause problems of model 
repeatability, one of the key fundamental requirements for the generation of a groundwater 
vulnerability model intended for critical policy and decision-making. 
 
Figure A5: Random subsampling and splitting of the dataset into training, validation and 
testing sets 
K-fold cross-validation 
In this technique, the dataset is first split into training-validation and testing datasets. Then the 
training-validation dataset is further split into a K number of folds, where K is the number of splits. 
The technique is almost similar to the random subsampling technique, with the only difference being 
that instead of splitting the train-validate dataset randomly, the dataset is split in a sequential manner, 
as shown in Figure A6. The number of folds is selected where, for a large number of folds, the bias 
of the validation error will be small but the variance will be large because the size of the test set will 
have been greatly reduced. The computation time will be longer for many folds. If a smaller-sized 
fold is used, the computation time is greatly reduced and the variance will be small, but the bias larger. 
Thus, the number of folds depends on the size of dataset — for a larger dataset, even the threefold 
approach gives good results. For a smaller dataset, the leave-one-out method is preferable. 
In machine learning, the tenfold method is the most common cross-validation method, as it offers a 
good compromise between processing time, bias and variance as the model is generated using over 
90% of the dataset. This makes it more likely to be generalisable to the full data spectrum. This benefit 
260 
 
 
of the tenfold cross-validation method was illustrated by Kohavi (1995) after comparing several 
approaches, including the leave-one-out, bootstrap and stratified tenfold approaches. 
 
Figure A6: K-fold cross-validation splitting of the dataset into training, validation and testing 
To avoid the generation of folds which do not account for ones and zeros in each fold, stratified k-
folding is used. 
Leave-one-out cross-validation 
In this technique, the dataset is first split into training-validation and testing datasets, after which the 
training-validation dataset is further split. The leave-one-out technique is a special case of the k-fold 
technique where the number of folds equals the number of instances in the datasets (Figure A7). Thus, 
for a dataset with N examples (points), N experiments are performed where, for each experiment, N-
1 examples are used for training while the remaining examples (points) are used for validation. 
261 
 
 
 
 Figure A7: Leave-one-out cross-validation splitting of the dataset into training, validation 
and testing 
The leave-one-out technique of splitting the training-validation dataset involves the following simple 
steps: 
11. For the given dataset, the first point (
) is extra¶cyted from the dataset as a validation dataset (

) and the remaining points as a training dataset ( 
). The model is run and the trained model is 
used to predict the value of th
e first validation point denoted 
ž
. This value is then compared with the actual ou„tp)ut value ( †
) and the difference between 
ž
 and 
†
 is returned as the validation error ( 
 . 
12. The extracted point is returned into the or„iginal dataset and the first step repeated, but this time using the second point ( !) and the error ! is g„en,e„rated as in the previous step. The process is repeated for all N training points and errors 
 !, ……,„M.
 returned. At the end of the 
splitting process, N errors are generated. A graph of „
, „!, …… „M.
 against 
, !, … . . , 
 is 
plotted and the best training split is the one with the fewest validation errors, as shown in Figure 
A8. 
In order to understand how the training/validation algorithm works, consider an example where a 
given dataset has four training points, as shown in Table A2. 
262 
 
 
Table A2: Example of a dataset with four points for running the leave-one-out cross-
validation technique 
 
The leave-one-out algorithm splits the dataset into training and validation datasets respectively, as 
shown in Table A3. 
Table A3: Data splitting of a four points example using the leave-one-out algorithm 
 
 
Figure A8: Leave-one-out cross-validation graph 
To improve the repeatability of the model generation and to reduce the computational time in the 
design of data-driven models for groundwater vulnerability, the assessment tools to be developed 
would first verify the number of examples (points) and then decide between K-fold cross-validation 
for large datasets and leave-one-out cross-validation for small datasets. 
 
 
 
263 
 
 
APPENDIX 4: EXAMPLE OF HOW THE BACKPROPAGATION 
ALGORITHM WORKS 
Consider a simple three-layer model with two inputs, a hidden layer with two neurons and one output, 
as shown in Figure A9:  
 
Figure A9: Example of how the back propagation algorithm works 
As an illustration of how the back propagation algorithm works, training using dataset A of the AND 
logic was done, where inputs y
 = 1, y! = 1 and the desired output j3 = 1. The bias was not used 
fo'rB Is=im( BIplicity. 'FBiIr=stB, Ithe feed-forward computations were done by calculating the output values ·
 and ·!) for each hidden layer neuron by applying the activation function to the sum 
of the weighted inputs. These values were then used to calculate the network output ('BI=BI¸3). 
'BI=BI·
 = v(y
 ∗ 
.
 + y! ∗ !.
) =  v(1 ∗ 0.4 + 1 ∗ 0.1) = v(0.5) =  (1 + 1..‚) = 0.6225 
'BI=BI·! = v(y
 ∗ 
.! + y! ∗ !.!) =  v(1 ∗ −0.1 + 1 ∗ −0.1) = v(−0.2) =  (1 +1.!) = 0.4502 
'BI=BI¸3 = v()
 ∗ 3.
 + )! ∗ 3.!) = v(0.6225 ∗ 0.06 + 0.4502 ∗ −0.4) = v(−0.14271) = 0.4644 
At this p>o>in<t>̧, the feed forward computations were complete. The next step was to calculate the output error ( 3) and to propagate it, backward)s to the hidden layer-output layer connections to calculate the new weights ( 3.
(M‘‹) 3.!(M‘‹) . 
>><>̧ 3 = '¸3 ∗ m1 − '¸3p ∗ m'Ÿ ¡‘ − '¸3p = 0.4643 ∗ (1 − 0.4643) ∗ (1 − 0.4643) = 0.13323 ∆3.
 = ¦ ∗ >><>̧ 3 ∗ )
 = 0.45 ∗ 0.13323 ∗ 0.6225 = 0.03732 3.
(M‘‹) = 3.
(‡©) + ∆3.
 + § ∗ ∆(I − 1) = 0.06 + 0.03732 + 0.9 ∗ 0 = 0.09714 
∆3.! = ¦ ∗ >><>̧ 3 ∗ )! = 0.45 ∗ 0.13323 ∗ 0.4502 = 0.02699 3.!(M‘‹) = 3.!(‡©) + ∆3.! + § ∗ ∆(I − 1) = −0.4 + 0.0699 + 0.9 ∗ 0 = −0.3730 
264 
 
 
Where ∆(I − 1) is zero for the first iteration. 
After calculating the new weights for the hidden layer-output layer connections, the next step was to 
propagate the error back to, the input layer-hidden layer con>n>e<c>̧tions. This was done by multiplying the new weights ( 3.
(M‘‹) 3.!(M‘‹)) by the output error ( 3), after which the delta changed in 
the weights (∆
.
, ∆!.
, ∆
.! and ∆!.!). The input layer-hidden layer neurons were calculated 
and, ultimately, the new input layer-hidden layer weights (
.
(M‘‹), !.
(M‘‹), 
.!(M‘‹) and !.!(M‘‹)) 
were computed. 
>><>·
 =  >><>̧>><> =  >><>̧ 3
∗ 
∗ 3.
(M‘‹) = 0.1332 ∗ 0.09713 = 0.012965 
·! 3 3.!(M‘‹) = 0.1332 ∗ −0.3730 = −0.04971 ∆ = ¦ ∗ >><> ∗ y = 0.45 ∗ 0.01296 ∗ 1 = 0.05834 
∆
.
 = ¦ ∗ >><>·
 ∗ y
 = 0.45 ∗ 0.01296 ∗ 1 = 0.05834 
∆ !.
.! =

 ¦ ∗ >><> ·
·! ∗ y
 =
! 0.45 ∗ −0.04971 ∗ 1 = −0.02237 
∆!.! = ¦ ∗ >><>·! ∗ y! = 0.45 ∗ −0.04971 ∗ 1 = −0.02237 
.
(M‘‹) = 
.
(‡©) + ∆
.
 + m§ ∗ ∆(I − 1)p = 0.4 + 0.005834 + 0.9 ∗ 0 = 0.4058 
!.
(M‘‹) = !.
(‡©) + ∆!.
 + m§ ∗ ∆(I − 1)p = 0.1 + 0.005834 + 0.9 ∗ 0 = 0.1054 

.!(M‘‹) = 
.!(‡©) + ∆
.! + m§ ∗ ∆(I − 1)p = −0.1 + (−0.02237) + 0.9 ∗ 0 = −0.1224 
!.!(M‘‹) = !.!(‡©) + ∆!.! + m§ ∗ ∆(I − 1)p = −0.1 + (−0.02237) + 0.9 ∗ 0 = −01224 
Once all the new weights had been calculated the same process was followed for training datasets B, 
C and D and the overall error for the first iteration could be calculated using the mean square error. 
For the second iteration (2), the weights from the first iteration were used: 
'BI=BI·
 = vmy
 ∗ 
.
(M‘‹) + y! ∗ !.
(M‘‹)p =  v(0.406 + 0.1) = 0.6236 
'BI=BI·! = vmy
 ∗ 
.!(M‘‹) + y! ∗ !.!(M‘‹)p =  v(−0.1224 − 0.122) = 0.4393 
'BI=BI¸3 (!) = vm)
 ∗ 3.
(M‘‹) + )! ∗ 3.!(M‘‹)p = v(0.6225 ∗ 0.097 + 0.4393 ∗ −0373) = 0.4714 
>><>̧ 3(!) = '¸=3(!0).1∗3m111−02'¸3(!)p ∗ m'Ÿ ¡‘ − '¸3(!)p = 0.4714 ∗ (1 − 0.4714) ∗ (1 − 0.4714) 
Thus, after the initial iteration, the calculated error was 0.133225 and the new calculated error was 
0.131102. Therefore, the algorithm had been improved, albeit not by much. However, this example 
should illustrate how the back propagation algorithm works. 
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APPENDIX 5: EXAMPLE OF HYBRID LEARNING OF THE ANFIS 
SYSTEM 
Let us  vconsider an example with two inputs 5, 6, with fuzzy memberships P, ‰, respectively and output . Two rules are defined, relating the inputs to the output given as: 
Rule 1: IF 5 is small (P
) AND 6 is small (‰
) THEN v
 is small, 
Rule 1: IF 5 is large (P!) AND 6 is large (‰!) THEN v
 is large. 
The hybrid learning protocol is 5us=ed3 with 6the= f4ollowing parameters to calculate the output of the trained network given the inputs  and . 
• bell function with parameters (/ = 2, J = 1, @
 = 1, @w
 = 2, @! = 9, @w! = 14, ) used to 
define the membership functions of the two inputs; and 
• 1co0e,f 0fici=en1ts0 o, >f th=e 1ou0tput membership function given by: =
 = 0.1,  0
 = 0.1,  >
 = 0.1,  =! =! ! . 
First, the calculations are calculated using Equation 7.9 to generate membership functions for each 
rule: 
n
(5) = 1 + ­51−2 1­! , nw
(6) = 1 + ­6
1−2 2­! 
n!(5) = 1 + ­51−2 9­! , nw!(6) = 1 + ­6
1−214­! 
Data are fed into the first layer where corresponding fuzzy membership values for each input are 
extracted from the membership function, as shown in Figure A10. The outputs from layer 1 are fed 
into layer 2, where they are summed to produce a result for each rule (Figure A11). The output from 
layer 2 then enters layer 3 and the data are normalised against all the other inputs to layer 3. The 
resultants are normalised values which are fed into layer 4. 
 
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Figure A10: Plot of fuzzy membership function for each of the rules 
 
Figure A11: Example of calculations and layer connections for layers 1, 2 and 3 
The normalised result from layer 3 enters layers 4 where it is combined with inputs using Equation 
7.4. The output of layer 4 then enters layer 5 where all the outputs from layer 4 of all the rules are 
summed together to produce one output result, using Equation 7.5. The output value is then compared 
with the actual value and the error is calculated and propagated backwards. The parameters are 
adjusted and the process continues until the error has been sufficiently reduced for the training process 
to be terminated. At that time the network is termed “trained” and will be ready for use in solving the 
particular problem. 
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Figure A12: Example of calculations and layer connections for layers 4 and 5 
 
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APPENDIX 6: GVAI SOFTWARE OPERATING MANUAL 
Program functionality 
The Groundwater Vulnerability Artificial Intelligence (GVAI) software is a computer program used 
for the generation of groundwater vulnerability models using the three most common AI algorithms 
(Fuzzy Expert system, Artificial Neural Networks (ANN) and the Adaptive Neuro-Fuzzy Inference 
System (ANFIS). 
The software also allows for automatic and semi-automatic processing and the generation of 
groundwater vulnerability models. The friendly interface of the software and many opportunities in 
the semi-automatic mode for AI modelling allows solving complex geological and hydrogeological 
conditions with great efficiency. The current version only runs on a IBM-PC compatible computers 
equipped with Windows. 
System requirements 
The GVAI software can be installed on a PC with OS Windows 98 and higher. The recommended 
system parameters are: 
• processor > 2 GHz; 
• memory at least 512 Mb; and 
• screen resolution of 1 024 x 768 colour mode. 
As the software actively uses the registry and writes in the C drive, it is recommended that the 
software be launched using administrator’s read/write rights. 
Program installations 
To install the program, copy the files from the CD and create a directory in the computer. Updating 
simply entails overwriting the previous directory with the new directory files. 
Program operation 
Launch page 
On the launch page the following can be done: 
• to access the GVAI software modules, click the button “LAUNCH PROGRAM” and the 
software opens the data input module; 
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• to access to the manual, click the “HELP” button and the software will open the manual file in 
pdf format; and 
• to access the software details and version, click the “ABOUT” button which will display a 
window. 
 
Figure A13: GVAI launch module 
Data input module 
The data input module facilitates loading all the relevant datasets and viewing them before proceeding 
to the other modules. This version of the software only works with (geotif) raster and (.csv) vector 
data types. The software only takes in the geotif which must comprise a similar number of rows, 
columns and grid cell sizes. Hence, it is strongly recommended that the user first prepare the input 
maps using GIS software such as ArcGIS, QGIS or MapINFO. 
Figure 8.3 shows the GUI of the data input window. First, load each of the ten raster map layers using 
the corresponding “Browse” button next to the map name and view the map by clicking the 
corresponding “Plot” button. Once all ten maps have been added to the program, the program will 
pose question “Are groundwater pollution data available?” 
If such data are indeed available, then click the “YES” button and the borehole point browse and plot 
buttons are enabled prompting the user to load this data file into the program. At the same time the 
previously disabled knowledge-driven approach (Fuzzy Expert system) and data-driven approaches 
(ANN and ANFIS) buttons are enabled. Thus, with the ten maps and pollution data loaded, the user 
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can execute both the knowledge and data-driven approaches. Alternatively, if the answer is “NO”, 
then only the knowledge-driven approach (Fuzzy Expert system) button will be enabled. 
Click the “RETURN TO HOME PAGE” button to return back to the launch page. This will refresh 
the entire program. 
Click the “HELP” button to open the user manual which describes and gives a detailed step by step 
outline of the program functions. 
Clicking the “ABOUT” leads the program to open a pop-up window which shows the software details 
including the version, copyright and disclaimer. 
A description of each of the ten input maps is given below: 
Rainfall - This map shows the rainfall distribution over a given area. The rainfall can be average long 
term, annual, monthly or a single rain event. The typical unit is millimetres (mm). 
Slope – This map shows the topographic change in slope expressed in percentage (%). This can be 
generated from any topographic data, but SRTM data are free to download from the Internet. 
Distance to surface sources – These map data refer to a distance map generated from mapped sources 
of surface sources. The sources can be mapped by physically recording GPS coordinates of potential 
sources and using this information to generate a distance map. Alternatively, the sources of AMD 
may be interpreted by using the mapping of the secondary iron-bearing minerals which are often 
indicators of AMD. 
Distance to subsurface sources – This map is a distance map derived from the geology map showing 
the rocks where there are coal seams within the study area. The vector geology polygon of the host 
should be extracted from the geology vector map and changed to raster format to create a distance 
map from the information. ArcGIS, QGIS and any other GIS can be used for the creation of the 
distance to subsurface sources map. 
Soil clay content – This map is a raster map showing the distribution of the soil clay over the study 
area. The clay content is expressed as a percentage values. 
Relative hydraulic conductivity – This map shows the relative hydraulic conductivity of various 
aquifers within the area to be modelled. The values are ranked between 1 and 10, where 10 is the 
aquifer with the highest and 1 the lowest hydraulic conductivity values. 
Distance to pathways – This map is a distance map derived from mapped lineaments from 
geophysical interpretation and/or geology maps. The vector lines of the lineaments are changed to 
raster format from which a “distance from pathway” map is created. ArcGIS, QGIS and any other 
GIS can be used to create the distance to subsurface maps. 
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Relative rock permeability – This map shows the relative permeability of various rocks within the 
area to be modelled. The values are ranked between 1 and 10, where a value of 10 is assigned to rocks 
with high permeability values and 1 is assigned to the rocks with the lowest permeability value. The 
values of permeability can be measured in the field or laboratory or extracted from publications. 
Relative rock-AMD reactivity – This map shows the relative hydraulic conductivity of various 
aquifers within the area to be modelled. The values are ranked between 1 and 10, where 10 is the 
aquifer with the highest and 1 the lowest hydraulic conductivity values. 
Depth to water table – This map shows the distance from the surface to the water table, as measured 
in boreholes within the area to be modelled. Data can be collected over the area to be modelled and 
interpolation methods used to create the map. 
Borehole points – The data format should be an .csv file in the following format: 
X Y SO4 Sulphate 
784154 6958117 1 0.4 
716826 7097336 0 256 
 
 
Figure A14: Input module window 
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Figure A15: About window 
As a demonstration of the functionality of the program, data for the Witbank, Ermelo and Highveld 
coalfield will be used. Using the steps for loading maps to the program, the following is an example 
of a view of the rainfall data in the program. 
 
Figure A16: Input module window 
Figure A16 presents a screen shot of the result when the plot button is pressed for a rainfall map layer. 
The window shows the spatial distribution of rainfall together with raster information (cell size, 
minimum, maximum and the number of rows and columns). 
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Figure A17: Input module window 
Figure A17 presents a screen shot of the window that pops up after loading boreholes and clicking 
the plot button. This view displays the spatial distribution of the points on the rainfall map. In addition, 
a small window is displayed showing the number of points in the input data file. 
Fuzzy Expert System Module 
The fuzzy expert System module is used to generate a fuzzy groundwater vulnerability model using 
the ten map raster layers from the input data module. The module allows the user to design the fuzzy 
membership function for each map layer according to expert knowledge on AMD processes in the 
study area. In addition, the user is able to execute automatic processing which relies on parameters, 
as outlined in Sakala et al. (2018). When designing the fuzzy expert system, the drop-down buttons 
are used to select values for the map@ _vHal/u5e (H) and confidence (@v), @_H/5 and @u_H7 for each of the corresponding map layers. The  u  value specifies the maximum values of  and the @_H7 value specifies the minimum value of  according to the equation below: 
no =  H ∗10@v00∗ u 
The steps for using the fuzzy module are as follows: 
1. In th_eH fu7zzy module, adjust the design parameters (map value (H), confidence (@v), @_H/5 and  ). 
2. Clicking on the corresponding “PLOT” button to view the fuzzy values for each map. 
274 
 
 
3. Once all the map layers have been converted to fuzzy values, specify the fuzzy operations 
(AND, OR, PRODUCT, GAMMA, SUM) reflecting the relationships between the map layers. 
4. Click the “PLOT” button next to each operator to view the output for that stage. The colour of 
the button changes to red (Figure A19). Figure A20 presents an example of the combination of 
the input of all the sources into one fuzzy map for sources (Figure A20). 
5. Select the map layer from folder C:\GVA_AI\Fuzzy for the sources, transport and traps and 
click the PLOT button on the far right to generate the combined output (Figure A21). The details 
of the map will also be displayed. 
 
Figure A18: Fuzzy expert system module window 
275 
 
 
 
Figure A19: Source output in fuzzy values 
 
Figure A20: Map output after combining all the inputs from the sources  
276 
 
 
 
Figure A21: Fuzzy expert system output map 
Data Pre-Processing Module for Data-Driven AI Systems 
The purpose of the data pre-processing module (Figure A22) is to prepare the data in a format which 
is comprehensible to the data-driven system facilitating the production of a binary map. Figure 8.7 
shows the GUI for the pre-processing module.  
The step for the data pre-processing are: 
1. Click on TEST button and a graph will appear, showing a cumulative graph (Figure A23). 
Use the cumulative graph to identify a range of values within which at least 50% of 
boreholes with a high sulphate concentration are found. If a test is complete, the test button 
turns red. Record the range of values for each map. 
2. Enter the values on the set threshold values section for each map and click the 
corresponding PLOT button. After the map is displayed the colour of the button changes 
to red. Once all the maps have been plotted each of the buttons will have turned to red. 
Then, click on the “CREATE TRAINING DATASET” button. The previously disabled 
“GO TO ARTIFICIAL NEURAL NETWORK” and “GO TO ADAPTIVE NEURO-
FUZZY INFERENCE SYSTEM” buttons will be enabled. 
277 
 
 
 
Figure A22: Data-driven artificial intelligence data pre-processing module window 
 
Figure A23: Spatial association test result 
Artificial Neural Networks Module 
The artificial neural network module receives data from the pre-processing module and computes the 
groundwater vulnerability model using the Artificial Neural Network (ANN) algorithm. Figure 10 
shows the GUI for ANN module and the results are shown in Figure 11. 
The steps for the production an ANN model are: 
1. Enter the number of neurons in the hidden layer and the number of training epochs (iterations) 
and select the activation function, 
2. Click the “RUN PROGRAM” button and graphs and the ANN model will also be displayed. 
278 
 
 
3. When clicking the “RUN AUTOMATIC TRAINING” button, the program will determine the 
number of hidden layers and epoch on its own. 
 
Figure A24: ANN module window 
 
Figure A25: Display of ANN results  
  
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Adaptive Neural-Fuzzy Inference System (ANFIS) Module 
This module runs the ANFIS hybrid algorithm to produce a groundwater vulnerability model. 
Figure 14 shows the GUI of the ANF module. The steps are: 
1. Enter the number of training epochs (iterations) and values of mean and sigma and select the 
activation function, 
2. Click the “RUN ANFIS” button and the output ANFIS model will be displayed (Figure 15), 
3. Selecting the automatic processing program will run the ANFIS algorithm using pre-set 
parameters. Then click the “RUN AUTOMATIC ANFIS PROCESSING” button and the 
program will determine the number of training epochs and generate the ANFIS model. 
 
Figure A26: Adaptive Neural-Fuzzy Inference System module window 
280 
 
 
 
Figure A27: Adaptive Neural-Fuzzy Inference module 
Model validation Module 
The model validation module statistically validates the generated AI models using a separate 
validation vector dataset. Figure A28 shows the GUI for the module. 
The steps for using the model validation module: 
1. Browse the validation vector data from their stored location in the computer, 
2. Search for the models produced: the data path is C:\GVAI\Fuzzy for the fuzzy module, 
C:\GVAI\ANN for the ANN model and C:\GVAI\ANFIS for the ANFIS model. The loaded 
models may be viewed by clicking of “PLOT” button of the corresponding model,  
3. Click the “VALIDATE” button on each of the models to display a correlation coefficient value, 
as shown in Figure A29. 
281 
 
 
 
Figure A28: Model comparison module 
 
Figure A29: Validation graph of the fuzzy model 
 
 
282 
 
 
ABSTRACT 
Despite groundwater being a very important and valuable source of water for humans it is under 
serious threat by human activities such as mining. Nevertheless, benefits of mining, in particular coal 
mining, have led to improvement in the social and economic development of many countries. 
However, despite the important benefits of coal to developing and developed countries, groundwater 
pollution caused by coal mining generated pollutants (acid mine drainage (AMD)) is a significant 
problem globally. Finding scientific solutions on how coal mining and coal waste disposal can be 
controlled and monitored from a policy and decision-making perspective in view of ultimately 
minimising the pollution of groundwater resources in coalfields is therefore an urgent imperative. 
This can be done by undertaking a coalfield-scale groundwater vulnerability assessment to rank areas 
in terms of the likelihood of pollutants reaching the groundwater. 
The research discusses the development of a new approach for groundwater vulnerability assessment 
specific to AMD at a regional coalfield scale using artificial intelligence to automate some of the 
processes and to assist in the generation of rapid groundwater vulnerability assessment results for use 
by policy and decision-makers in controlling coal mining and coal waste disposal in a typical 
coalfield. The approach is a hybrid of the index and overlay, process-based simulation and statistical 
approaches generated by combining factors associated with pollutant sources, energy that drives the 
pollution migration and the ways AMD pollution interacts with the subsurface both physically and 
chemically. Laboratory analyses (rock-AMD reactivity, soil batch leach tests) and fieldwork (water 
sampling, ground geophysics) were done to generate the input map layers and to validate the produced 
results. 
The modified approach is illustrated through a discussion of a case study of AMD pollution in the 
Witbank, Ermelo and Highveld coalfields of the Mpumalanga and KwaZulu-Natal Provinces in South 
Africa. Many AMD cases have been reported in these provinces in recent years and are a cause of 
concern for local municipalities, mining and environmental agencies. In the Witbank, Ermelo and 
Highveld coalfields, several areas have been mined out while mining has not yet started in others, 
hence the need to identify groundwater regions prone to AMD pollution in order to avoid further 
impacts on the groundwater resources. 
A knowledge-based fuzzy expert system, an artificial neural network (ANN) system and an adaptive 
neuro-fuzzy inference system (ANFIS) were built using vulnerability factors (energy sources, ligands 
sources, pollutant sources, transportation pathways and traps) to generate groundwater vulnerability 
models of the coalfields. Highly vulnerable areas were identified in the Witbank coalfield and the 
eastern part of the Ermelo coalfield which are characterised by the presence of AMD sources and 
283 
 
 
good subsurface transport coupled with poor AMD pollution trapping properties. The results from all 
three AI systems show a strong positive correlation of over 0.8 with groundwater sulphate 
concentrations from two different datasets. In addition, relationships between geophysical responses 
(resistivity and seismic velocity) and model values were obtained and used to validate the models. 
The results show that the proposed approach can indeed be used for groundwater vulnerability 
assessment. 
As a summary of the AI system, a toolbox containing all the tools needed for AI modelling of 
groundwater vulnerability was developed. The toolbox is flexible and works both for manual and 
semi-automatic processing allowing the user to contribute to the decisions taken in the modelling. 
The toolbox serves to automate many processes associated with this type of modelling, resulting in 
higher processing speed and improved accuracy in the generation of the model. 
The methodology only considers the AMD pollution attenuation and migration at a regional scale and 
does not account for local-scale sources of pollution and attenuation. Further research to refine the 
approach may include the incorporation of groundwater flow direction and temporal datasets for the 
future prediction of groundwater vulnerability. The approach may also be applied to other coalfields 
to assess its robustness to changing hydrogeological conditions. 
KEYWORDS: Artificial Intelligence, Groundwater Vulnerability, Algorithm, Fuzzy Expert System, 
Artificial Neural Network, Adaptive Neuro-Fuzzy Inference System 
 
 
 
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